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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A generalization of a theorem on naturally reductive homogeneous spaces


Authors: Oldřich Kowalski and Lieven Vanhecke
Journal: Proc. Amer. Math. Soc. 91 (1984), 433-435
MSC: Primary 53C30
MathSciNet review: 744644
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Abstract: We prove that a homogeneous Riemannian manifold all of whose geodesics are orbits of one-parameter subgroups of isometries has volume-preserving local geodesic symmetries.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744644-7
PII: S 0002-9939(1984)0744644-7
Keywords: Naturally reductive homogeneous spaces, commutative spaces, generalized Heisenberg groups, volume-preserving geodesic symmetries, orbits of one-parameter subgroups
Article copyright: © Copyright 1984 American Mathematical Society