The Manifold of Conformally Equivalent Metrics

Abstract

Ebin [8] gives a thorough study of the spaceof riemannian metrics on a compact manifoldMand of the action of the diffeomorphism groupofMon. The purpose of this paper is to study the action of the larger groupof conformorphisms, or conformai transformations, onand on. On, the L₂-orthogonal decomposition induced by the action ofgives a splitting of symmetric tensors into three summands introduced by York [25;26]. We find submanifolds oftangent to the pieces of this decomposition.