Asian Journal of Mathematics

Volume 14 (2010)

Number 3

Codazzi-equivalent Riemannian Metrics

Pages: 291 – 302



Angela Schwenk-Schellschmidt

Udo Simon

Luc Vrancken


On a smooth manifold $M$ we introduce the concept of Codazzi-equivalent Riemannian metrics. The curvature tensors of two Codazzi-equivalent metrics satisfy a simple relation. The results together with known facts about Codazzi tensors give a method of proof for old and new local and global uniqueness results for Riemannian manifolds and Euclidean hypersurfaces.


Codazzi-equivalent Riemannian metrics; Codazzi tensors; hypersurfaces with parallel normals

2010 Mathematics Subject Classification

53B20, 53B21, 53C20, 53C21

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