Continuous actions of compact Lie groups on Riemannian manifolds

Abstract

M. H. A. Newman proved that if M is a connected topological manifold with metric d, there exists a number E > 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 e. 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 e in terms of convexity and curvature invariants of M.