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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The fine structure of transitive Riemannian isometry groups. I


Authors: Carolyn S. Gordon and Edward N. Wilson
Journal: Trans. Amer. Math. Soc. 289 (1985), 367-380
MSC: Primary 53C30
MathSciNet review: 779070
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Abstract: Let $ M$ be a connected homogeneous Riemannian manifold, $ G$ the identity component of the full isometry group of $ M$ and $ H$ a transitive connected subgroup of $ G$. $ G = HL$, where $ L$ is the isotropy group at some point of $ M$. $ M$ is naturally identified with the homogeneous space $ H/H \cap L$ endowed with a suitable left-invariant Riemannian metric. This paper addresses the problem: Given a realization of $ M$ as a Riemannian homogeneous space of a connected Lie group $ H$, describe the structure of the full connected isometry group $ G$ in terms of $ H$. This problem has already been studied in case $ H$ is compact, semisimple of noncompact type, or solvable. We use the fact that every Lie group is a product of subgroups of these three types in order to study the general case.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0779070-3
PII: S 0002-9947(1985)0779070-3
Keywords: Isometry groups, homogeneous Riemannian manifolds, Levi decompositions
Article copyright: © Copyright 1985 American Mathematical Society