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

 

Continuous actions of compact Lie groups on Riemannian manifolds


Authors: David Hoffman and L. N. Mann
Journal: Proc. Amer. Math. Soc. 60 (1976), 343-348
MSC: Primary 57E10
MathSciNet review: 0423386
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0423386-7
PII: S 0002-9939(1976)0423386-7
Keywords: Newman's theorem on periodic transformations, diameter of orbits, radius of convexity
Article copyright: © Copyright 1976 American Mathematical Society