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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- © 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