Bounded isometries and homogeneous Riemannian quotient manifolds

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 M is homogeneous if and only if consists of Clifford translations of M. The technique of proof also leads to a determination of the group of all isometries of M.IMAF, Córdoba, Argentina. Partially supported by Conicet, Argentina, and by IMPA, Rio de Janeiro, Brazil.IMAF, Córdoba, Argentina. Partially supported by Conicet, Argentina.University of California at Berkely, U.S.A. Partially supported by National Science Foundation Grant DMS-8200235.