Bounded isometries and homogeneous Riemannian quotient manifolds

Abstract

Let M be a Riemannian manifold that admits a transitive semisimple group G′ of isometries, G′ of noncompact type. Then every bounded isometry of M centralizes G′ and so is a Clifford translation (constant displacement). Thus a Riemannian quotient Γ∖M is homogeneous if and only if Γ consists of Clifford translations of M. The technique of proof also leads to a determination of the group of all isometries of M.