CONFORMALLY FLAT HYPERSURFACES IN REAL SPACE FORMS WITH LEAST TENSION

Abstract

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which receives the least possible amount of tension imposed on the submanifold from the ambient space. The purpose of this paper is to classify conformally flat ideal hypersurfaces in real space forms; thus we completely determine conformally flat manifolds which admit codimension one isometric immersions into real space forms with least possible tension.