NDLI: Totally geodesic singular orbits and symmetric singular orbits in cohomogeneity one Riemannian manifolds

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Totally geodesic singular orbits and symmetric singular orbits in cohomogeneity one Riemannian manifolds

Content Provider	Springer Nature Link
Author	Abedi, H. Alekseevsky, D. V. Kashani, S. M. B.
Copyright Year	2008
Abstract	We classify cohomogeneity one G-manifolds M of a simple Lie group G such that one of the singular orbits is a simply connected symmetric space. We give a simple necessary and sufficient condition that a singular orbit P of a cohomogeneity one Riemannian G-manifold is totally geodesic. Using it, we obtain a list of cohomogeneity one G-manifolds M as above such that the singular orbit P is totally geodesic with respect to any G-invariant Riemannian metric of M. Such G-manifolds have no G-invariant metric of positive or negative curvature if the rank of the symmetric space P is greater than one.
Starting Page	193
Ending Page	205
Page Count	13
File Format	PDF
ISSN	19950802
Journal	Lobachevskii Journal of Mathematics
Volume Number	29
Issue Number	4
e-ISSN	18189962
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2008-11-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	cohomogeneity one Riemannian manifolds cohomogeneity one actions of a semisimple Lie group singular orbits totally geodesic submanifolds Homogeneous manifolds Groups acting on specific manifolds Probability Theory and Stochastic Processes Mathematical Logic and Foundations Geometry Analysis Algebra Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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