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Transformation Groups with (n-1)-Dimensional Orbits on Non-Compact Manifolds

Published online by Cambridge University Press:  22 January 2016

Tadashi Nagano
Tadashi Nagano*
Affiliation:
Mathematical Institute, University of Tokyo
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When a Lie group G operates on a differentiable manifold M as a Lie transformation group, the orbit of a point p in M under G, or the G-orbit of p, is by definition the submanifold G(p) = {G(p); g∈G}. The purpose of this paper is to characterize the structure of a non-compact manifold M such that there exists a compact orbit of dimension (n — 1), n — dim M, under a connected Lie transformation group G, which is assumed to be compact or an isometry group of a Riemannian metric on M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 14 , February 1959 , pp. 25 - 38
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

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