Generalized normal homogeneous Riemannian metrics on spheres and projective spaces
Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on...
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| Autor*in: |
Berestovskiĭ, Valeriĭ Nikolaevich [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds Normal homogeneous Riemannian manifolds |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of global analysis and geometry - Springer Netherlands, 1983, 45(2013), 3 vom: 03. Aug., Seite 167-196 |
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| Übergeordnetes Werk: |
volume:45 ; year:2013 ; number:3 ; day:03 ; month:08 ; pages:167-196 |
| Links: |
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| DOI / URN: |
10.1007/s10455-013-9393-x |
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| Katalog-ID: |
OLC2060262461 |
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| 100 | 1 | |a Berestovskiĭ, Valeriĭ Nikolaevich |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Generalized normal homogeneous Riemannian metrics on spheres and projective spaces |
| 264 | 1 | |c 2013 | |
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| 520 | |a Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). | ||
| 650 | 4 | |a Clifford algebras | |
| 650 | 4 | |a Clifford–Wolf homogeneous spaces | |
| 650 | 4 | |a Generalized normal homogeneous Riemannian manifolds | |
| 650 | 4 | |a g.o. spaces | |
| 650 | 4 | |a Grassmannian algebra | |
| 650 | 4 | |a Homogeneous spaces | |
| 650 | 4 | |a Hopf fibrations | |
| 650 | 4 | |a Normal homogeneous Riemannian manifolds | |
| 650 | 4 | |a Generalized normal homogeneous but not normal homogeneous | |
| 650 | 4 | |a Riemannian submersions | |
| 650 | 4 | |a (weakly) symmetric spaces | |
| 700 | 1 | |a Nikonorov, Yuriĭ Gennadievich |4 aut | |
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10.1007/s10455-013-9393-x doi (DE-627)OLC2060262461 (DE-He213)s10455-013-9393-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskiĭ, Valeriĭ Nikolaevich verfasserin aut Generalized normal homogeneous Riemannian metrics on spheres and projective spaces 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces Nikonorov, Yuriĭ Gennadievich aut Enthalten in Annals of global analysis and geometry Springer Netherlands, 1983 45(2013), 3 vom: 03. Aug., Seite 167-196 (DE-627)12986224X (DE-600)283662-2 (DE-576)015173666 0232-704X nnns volume:45 year:2013 number:3 day:03 month:08 pages:167-196 https://doi.org/10.1007/s10455-013-9393-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 AR 45 2013 3 03 08 167-196 |
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10.1007/s10455-013-9393-x doi (DE-627)OLC2060262461 (DE-He213)s10455-013-9393-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskiĭ, Valeriĭ Nikolaevich verfasserin aut Generalized normal homogeneous Riemannian metrics on spheres and projective spaces 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces Nikonorov, Yuriĭ Gennadievich aut Enthalten in Annals of global analysis and geometry Springer Netherlands, 1983 45(2013), 3 vom: 03. Aug., Seite 167-196 (DE-627)12986224X (DE-600)283662-2 (DE-576)015173666 0232-704X nnns volume:45 year:2013 number:3 day:03 month:08 pages:167-196 https://doi.org/10.1007/s10455-013-9393-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 AR 45 2013 3 03 08 167-196 |
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10.1007/s10455-013-9393-x doi (DE-627)OLC2060262461 (DE-He213)s10455-013-9393-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskiĭ, Valeriĭ Nikolaevich verfasserin aut Generalized normal homogeneous Riemannian metrics on spheres and projective spaces 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces Nikonorov, Yuriĭ Gennadievich aut Enthalten in Annals of global analysis and geometry Springer Netherlands, 1983 45(2013), 3 vom: 03. Aug., Seite 167-196 (DE-627)12986224X (DE-600)283662-2 (DE-576)015173666 0232-704X nnns volume:45 year:2013 number:3 day:03 month:08 pages:167-196 https://doi.org/10.1007/s10455-013-9393-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 AR 45 2013 3 03 08 167-196 |
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10.1007/s10455-013-9393-x doi (DE-627)OLC2060262461 (DE-He213)s10455-013-9393-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskiĭ, Valeriĭ Nikolaevich verfasserin aut Generalized normal homogeneous Riemannian metrics on spheres and projective spaces 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces Nikonorov, Yuriĭ Gennadievich aut Enthalten in Annals of global analysis and geometry Springer Netherlands, 1983 45(2013), 3 vom: 03. Aug., Seite 167-196 (DE-627)12986224X (DE-600)283662-2 (DE-576)015173666 0232-704X nnns volume:45 year:2013 number:3 day:03 month:08 pages:167-196 https://doi.org/10.1007/s10455-013-9393-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 AR 45 2013 3 03 08 167-196 |
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10.1007/s10455-013-9393-x doi (DE-627)OLC2060262461 (DE-He213)s10455-013-9393-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskiĭ, Valeriĭ Nikolaevich verfasserin aut Generalized normal homogeneous Riemannian metrics on spheres and projective spaces 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces Nikonorov, Yuriĭ Gennadievich aut Enthalten in Annals of global analysis and geometry Springer Netherlands, 1983 45(2013), 3 vom: 03. Aug., Seite 167-196 (DE-627)12986224X (DE-600)283662-2 (DE-576)015173666 0232-704X nnns volume:45 year:2013 number:3 day:03 month:08 pages:167-196 https://doi.org/10.1007/s10455-013-9393-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 AR 45 2013 3 03 08 167-196 |
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Enthalten in Annals of global analysis and geometry 45(2013), 3 vom: 03. Aug., Seite 167-196 volume:45 year:2013 number:3 day:03 month:08 pages:167-196 |
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Enthalten in Annals of global analysis and geometry 45(2013), 3 vom: 03. Aug., Seite 167-196 volume:45 year:2013 number:3 day:03 month:08 pages:167-196 |
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Clifford algebras Clifford–Wolf homogeneous spaces Generalized normal homogeneous Riemannian manifolds g.o. spaces Grassmannian algebra Homogeneous spaces Hopf fibrations Normal homogeneous Riemannian manifolds Generalized normal homogeneous but not normal homogeneous Riemannian submersions (weakly) symmetric spaces |
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Berestovskiĭ, Valeriĭ Nikolaevich @@aut@@ Nikonorov, Yuriĭ Gennadievich @@aut@@ |
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ddc 510 ssgn 17,1 misc Clifford algebras misc Clifford–Wolf homogeneous spaces misc Generalized normal homogeneous Riemannian manifolds misc g.o. spaces misc Grassmannian algebra misc Homogeneous spaces misc Hopf fibrations misc Normal homogeneous Riemannian manifolds misc Generalized normal homogeneous but not normal homogeneous misc Riemannian submersions misc (weakly) symmetric spaces |
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Generalized normal homogeneous Riemannian metrics on spheres and projective spaces |
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Berestovskiĭ, Valeriĭ Nikolaevich |
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generalized normal homogeneous riemannian metrics on spheres and projective spaces |
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Generalized normal homogeneous Riemannian metrics on spheres and projective spaces |
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Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). © Springer Science+Business Media Dordrecht 2013 |
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Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). © Springer Science+Business Media Dordrecht 2013 |
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Abstract In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres $${S^n}$$. We prove that for any connected (almost effective) transitive on $$S^n$$ compact Lie group $$G$$, the family of $$G$$-invariant Riemannian metrics on $$S^n$$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $$n\ge 5$$. Any such family (that exists only for $$n=2k+1$$) contains a metric $$g_\mathrm{can}$$ of constant sectional curvature $$1$$ on $$S^n$$. We also prove that $$(S^{2k+1}, g_\mathrm{can})$$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $$G$$ (except the groups $$G={ SU}(k+1)$$ with odd $$k+1$$). The space of unit Killing vector fields on $$(S^{2k+1}, g_\mathrm{can})$$ from Lie algebra $$\mathfrak g $$ of Lie group $$G$$ is described as some symmetric space (except the case $$G=U(k+1)$$ when one obtains the union of all complex Grassmannians in $$\mathbb{C }^{k+1}$$). © Springer Science+Business Media Dordrecht 2013 |
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