Continuous actions of compact Lie groups on Riemannian manifolds
Authors:
David Hoffman and L. N. Mann
Journal:
Proc. Amer. Math. Soc. 60 (1976), 343348
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 , 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 . 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 in terms of convexity and curvature invariants of M.
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 M. C. Ku, Newman's theorem for compact Riemannian manifolds, University of Massachusetts (preprint).
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 L. N. Mann and J. L. Sicks, Newman's theorem in the Riemannian category, Trans. Amer. Math. Soc. 210 (1975), 259266. MR 0423388 (54:11367)
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 M. H. A. Newman, A theorem on periodic transformations of spaces, Quart. J. Math. 2 (1931), 19.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197604233867
PII:
S 00029939(1976)04233867
Keywords:
Newman's theorem on periodic transformations,
diameter of orbits,
radius of convexity
Article copyright:
© Copyright 1976
American Mathematical Society
