Continuous actions of compact Lie groups on Riemannian manifolds

Hoffman, David; Mann, L. N.

doi:10.1090/S0002-9939-1976-0423386-7

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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A theorem on periodic transformations of spaces

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