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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuous actions of compact Lie groups on Riemannian manifolds
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by David Hoffman and L. N. Mann PDF
Proc. Amer. Math. Soc. 60 (1976), 343-348 Request permission

Abstract:

M. H. A. Newman proved that if M is a connected topological manifold with metric d, there exists a number $\varepsilon > 0$, depending only upon M and d, such that every compact Lie group acting effectively on M has at least one orbit of diameter at least $\varepsilon$. In this paper the authors consider the case where M is a Riemannian manifold and d is the distance function on M arising from the Riemannian metric. They obtain estimates for $\varepsilon$ in terms of convexity and curvature invariants of M.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 343-348
  • MSC: Primary 57E10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0423386-7
  • MathSciNet review: 0423386