Symmetric cut loci in riemannian manifolds

Abstract

Let M be a compact Riemannian manifold with Hl(M, Z) = 0. We show that, for a point p ∈ M, the cut locus and conjugate locus of p must intersect if M admits a group of isometries which fixes p and has principal orbits of codimension at most 2. This is a classical theorem of Myers [5] in the case when M has dimension 2. © 1985 American Mathematical Society.