Solution of a Busemann problem
Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncom...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Berestovskii, V.N. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
aspheric homogeneous Riemannian manifold Lie group with a left-invariant metric |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2010 |
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| Übergeordnetes Werk: |
Enthalten in: Siberian mathematical journal - SP MAIK Nauka/Interperiodica, 1966, 51(2010), 6 vom: Nov., Seite 962-970 |
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| Übergeordnetes Werk: |
volume:51 ; year:2010 ; number:6 ; month:11 ; pages:962-970 |
| Links: |
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| DOI / URN: |
10.1007/s11202-010-0095-3 |
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| Katalog-ID: |
OLC2033384322 |
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| 520 | |a Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). | ||
| 650 | 4 | |a Busemann | |
| 650 | 4 | |a -space | |
| 650 | 4 | |a geodesic | |
| 650 | 4 | |a aspheric homogeneous Riemannian manifold | |
| 650 | 4 | |a Lie group with a left-invariant metric | |
| 650 | 4 | |a geodesic orbit space | |
| 650 | 4 | |a isotropic homogeneous Riemannian manifold | |
| 650 | 4 | |a Euclidean space | |
| 650 | 4 | |a symmetric Riemannian space of rank 1 | |
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10.1007/s11202-010-0095-3 doi (DE-627)OLC2033384322 (DE-He213)s11202-010-0095-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskii, V.N. verfasserin aut Solution of a Busemann problem 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2010 Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). Busemann -space geodesic aspheric homogeneous Riemannian manifold Lie group with a left-invariant metric geodesic orbit space isotropic homogeneous Riemannian manifold Euclidean space symmetric Riemannian space of rank 1 Enthalten in Siberian mathematical journal SP MAIK Nauka/Interperiodica, 1966 51(2010), 6 vom: Nov., Seite 962-970 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:51 year:2010 number:6 month:11 pages:962-970 https://doi.org/10.1007/s11202-010-0095-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 51 2010 6 11 962-970 |
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10.1007/s11202-010-0095-3 doi (DE-627)OLC2033384322 (DE-He213)s11202-010-0095-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskii, V.N. verfasserin aut Solution of a Busemann problem 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2010 Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). Busemann -space geodesic aspheric homogeneous Riemannian manifold Lie group with a left-invariant metric geodesic orbit space isotropic homogeneous Riemannian manifold Euclidean space symmetric Riemannian space of rank 1 Enthalten in Siberian mathematical journal SP MAIK Nauka/Interperiodica, 1966 51(2010), 6 vom: Nov., Seite 962-970 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:51 year:2010 number:6 month:11 pages:962-970 https://doi.org/10.1007/s11202-010-0095-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 51 2010 6 11 962-970 |
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10.1007/s11202-010-0095-3 doi (DE-627)OLC2033384322 (DE-He213)s11202-010-0095-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskii, V.N. verfasserin aut Solution of a Busemann problem 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2010 Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). Busemann -space geodesic aspheric homogeneous Riemannian manifold Lie group with a left-invariant metric geodesic orbit space isotropic homogeneous Riemannian manifold Euclidean space symmetric Riemannian space of rank 1 Enthalten in Siberian mathematical journal SP MAIK Nauka/Interperiodica, 1966 51(2010), 6 vom: Nov., Seite 962-970 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:51 year:2010 number:6 month:11 pages:962-970 https://doi.org/10.1007/s11202-010-0095-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 51 2010 6 11 962-970 |
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10.1007/s11202-010-0095-3 doi (DE-627)OLC2033384322 (DE-He213)s11202-010-0095-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berestovskii, V.N. verfasserin aut Solution of a Busemann problem 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2010 Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). Busemann -space geodesic aspheric homogeneous Riemannian manifold Lie group with a left-invariant metric geodesic orbit space isotropic homogeneous Riemannian manifold Euclidean space symmetric Riemannian space of rank 1 Enthalten in Siberian mathematical journal SP MAIK Nauka/Interperiodica, 1966 51(2010), 6 vom: Nov., Seite 962-970 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:51 year:2010 number:6 month:11 pages:962-970 https://doi.org/10.1007/s11202-010-0095-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 51 2010 6 11 962-970 |
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Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). © Pleiades Publishing, Ltd. 2010 |
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Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). © Pleiades Publishing, Ltd. 2010 |
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Abstract We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). © Pleiades Publishing, Ltd. 2010 |
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