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Newman's theorem for compact Riemannian manifolds


Author: Mei Chin Ku
Journal: Proc. Amer. Math. Soc. 58 (1976), 343-346
MSC: Primary 57E15; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1976-0415645-9
MathSciNet review: 0415645
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Abstract: M. H. A. Newman has shown the following theorem: Let $ M$ be a connected topological manifold with a given metric. Then there is an $ \varepsilon > 0$ such that for every nontrivial action of a compact Lie group $ G$ on $ M$, there exists an orbit of diameter at least $ \varepsilon $. We obtain the best possible estimate of $ \varepsilon $ for the isometric actions of $ G$ on compact connected Riemannian manifolds.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0415645-9
Keywords: Cut locus, geodesic, infinitesimal variation, Ricci tensor, sectional curvature
Article copyright: © Copyright 1976 American Mathematical Society

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