A geometric splitting theorem for actions of semisimple Lie groups

Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Rosales-Ortega, José [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Bi-invariant metric Pseudo-Riemannian Semisimple Lie group Topologically transitive action

Anmerkung:	© The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021

Übergeordnetes Werk:	Enthalten in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg - Berlin [u.a.] : Springer, 1922, 91(2021), 2 vom: 07. Juni, Seite 287-296
Übergeordnetes Werk:	volume:91 ; year:2021 ; number:2 ; day:07 ; month:06 ; pages:287-296

Links:	Volltext

DOI / URN:	10.1007/s12188-021-00242-2

Katalog-ID:	SPR045654980

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520			\|a Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$.
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912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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Indexfelder

author_variant	j r o jro
matchkey_str	article:18658784:2021----::goercpitntermoatosfei
hierarchy_sort_str	2021
bklnumber	31.00
publishDate	2021
allfields	10.1007/s12188-021-00242-2 doi (DE-627)SPR045654980 (SPR)s12188-021-00242-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Rosales-Ortega, José verfasserin aut A geometric splitting theorem for actions of semisimple Lie groups 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021 Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213 Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Berlin [u.a.] : Springer, 1922 91(2021), 2 vom: 07. Juni, Seite 287-296 (DE-627)327579781 (DE-600)2044664-0 1865-8784 nnns volume:91 year:2021 number:2 day:07 month:06 pages:287-296 https://dx.doi.org/10.1007/s12188-021-00242-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 91 2021 2 07 06 287-296
spelling	10.1007/s12188-021-00242-2 doi (DE-627)SPR045654980 (SPR)s12188-021-00242-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Rosales-Ortega, José verfasserin aut A geometric splitting theorem for actions of semisimple Lie groups 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021 Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213 Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Berlin [u.a.] : Springer, 1922 91(2021), 2 vom: 07. Juni, Seite 287-296 (DE-627)327579781 (DE-600)2044664-0 1865-8784 nnns volume:91 year:2021 number:2 day:07 month:06 pages:287-296 https://dx.doi.org/10.1007/s12188-021-00242-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 91 2021 2 07 06 287-296
allfields_unstemmed	10.1007/s12188-021-00242-2 doi (DE-627)SPR045654980 (SPR)s12188-021-00242-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Rosales-Ortega, José verfasserin aut A geometric splitting theorem for actions of semisimple Lie groups 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021 Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213 Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Berlin [u.a.] : Springer, 1922 91(2021), 2 vom: 07. Juni, Seite 287-296 (DE-627)327579781 (DE-600)2044664-0 1865-8784 nnns volume:91 year:2021 number:2 day:07 month:06 pages:287-296 https://dx.doi.org/10.1007/s12188-021-00242-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 91 2021 2 07 06 287-296
allfieldsGer	10.1007/s12188-021-00242-2 doi (DE-627)SPR045654980 (SPR)s12188-021-00242-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Rosales-Ortega, José verfasserin aut A geometric splitting theorem for actions of semisimple Lie groups 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021 Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213 Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Berlin [u.a.] : Springer, 1922 91(2021), 2 vom: 07. Juni, Seite 287-296 (DE-627)327579781 (DE-600)2044664-0 1865-8784 nnns volume:91 year:2021 number:2 day:07 month:06 pages:287-296 https://dx.doi.org/10.1007/s12188-021-00242-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 91 2021 2 07 06 287-296
allfieldsSound	10.1007/s12188-021-00242-2 doi (DE-627)SPR045654980 (SPR)s12188-021-00242-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Rosales-Ortega, José verfasserin aut A geometric splitting theorem for actions of semisimple Lie groups 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021 Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213 Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Berlin [u.a.] : Springer, 1922 91(2021), 2 vom: 07. Juni, Seite 287-296 (DE-627)327579781 (DE-600)2044664-0 1865-8784 nnns volume:91 year:2021 number:2 day:07 month:06 pages:287-296 https://dx.doi.org/10.1007/s12188-021-00242-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 91 2021 2 07 06 287-296
language	English
source	Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 91(2021), 2 vom: 07. Juni, Seite 287-296 volume:91 year:2021 number:2 day:07 month:06 pages:287-296
sourceStr	Enthalten in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 91(2021), 2 vom: 07. Juni, Seite 287-296 volume:91 year:2021 number:2 day:07 month:06 pages:287-296
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Bi-invariant metric Pseudo-Riemannian Semisimple Lie group Topologically transitive action
dewey-raw	510
isfreeaccess_bool	false
container_title	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
authorswithroles_txt_mv	Rosales-Ortega, José @@aut@@
publishDateDaySort_date	2021-06-07T00:00:00Z
hierarchy_top_id	327579781
dewey-sort	3510
id	SPR045654980
language_de	englisch
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author	Rosales-Ortega, José
spellingShingle	Rosales-Ortega, José ddc 510 bkl 31.00 misc Bi-invariant metric misc Pseudo-Riemannian misc Semisimple Lie group misc Topologically transitive action A geometric splitting theorem for actions of semisimple Lie groups
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topic_title	510 ASE 31.00 bkl A geometric splitting theorem for actions of semisimple Lie groups Bi-invariant metric (dpeaa)DE-He213 Pseudo-Riemannian (dpeaa)DE-He213 Semisimple Lie group (dpeaa)DE-He213 Topologically transitive action (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc Bi-invariant metric misc Pseudo-Riemannian misc Semisimple Lie group misc Topologically transitive action
topic_unstemmed	ddc 510 bkl 31.00 misc Bi-invariant metric misc Pseudo-Riemannian misc Semisimple Lie group misc Topologically transitive action
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title	A geometric splitting theorem for actions of semisimple Lie groups
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title_full	A geometric splitting theorem for actions of semisimple Lie groups
author_sort	Rosales-Ortega, José
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journalStr	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
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title_sort	geometric splitting theorem for actions of semisimple lie groups
title_auth	A geometric splitting theorem for actions of semisimple Lie groups
abstract	Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021
abstractGer	Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021
abstract_unstemmed	Abstract Let M be a compact connected smooth pseudo-Riemannian manifold that admits a topologically transitive G-action by isometries, where %$G = G_1 \ldots G_l%$ is a connected semisimple Lie group without compact factors whose Lie algebra is %${\mathfrak {g}}= {\mathfrak {g}}_1 \oplus {\mathfrak {g}}_2 \oplus \cdots \oplus {\mathfrak {g}}_l%$. If %$m_0,n_0,n_0^i%$ are the dimensions of the maximal lightlike subspaces tangent to M, G, %$G_i%$, respectively, then we study G-actions that satisfy the condition %$m_0=n_0^1 + \cdots + n_0^{l}%$. This condition implies that the orbits are non-degenerate for the pseudo Riemannian metric on M and this allows us to consider the normal bundle to the orbits. Using the properties of the normal bundle to the G-orbits we obtain an isometric splitting of M by considering natural metrics on each %$G_i%$. © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021
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container_issue	2
title_short	A geometric splitting theorem for actions of semisimple Lie groups
url	https://dx.doi.org/10.1007/s12188-021-00242-2
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doi_str	10.1007/s12188-021-00242-2
up_date	2024-07-03T17:26:43.682Z
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A geometric splitting theorem for actions of semisimple Lie groups

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