Asian Journal of Mathematics

Volume 14 (2010)

Number 3

Codazzi-equivalent Riemannian Metrics

Pages: 291 – 302

DOI: http://dx.doi.org/10.4310/AJM.2010.v14.n3.a1

Authors

Angela Schwenk-Schellschmidt

Udo Simon

Luc Vrancken

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

53B20, 53B21, 53C20, 53C21

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