Hypersurfaces and Codazzi tensors
  In this paper we deal with the following problem: Find all Riemannian metrics on a manifold that can be realized isometrically as immersed hypersurfaces in the Euclidean space. We study this problem for a wide class of metrics on hypersurfaces arising from Codazzi tensors. 
Thomas Hasanis and Theodoros Vlachos