Codazzi-equivalent Riemannian metrics
The concept of Codazzi-equivalent Riemannian metrics is introduced. Then, a simple relation on the curvature tensors of two Codazzi-equivalent metrics is deduced. This implies some local and global uniqueness results for Riemannian manifolds and Euclidean hypersurfaces with maximal rank of the shape operator.
Codazzi-equivalence of Riemannian metrics
scientific article; zbMATH DE number 5858625