Conformal de Rham decomposition of Riemannian manifolds

Details Conformal de Rham decomposition of Riemannian manifolds Conformal de Rham decomposition of Riemannian manifolds

2004-04-23

arxiv.org/abs/math/0404434v1

Mathematics

Differential Geometry

17 pages

Scientific paper

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We also obtain other related de Rham-type decomposition theorems. As an application, we study Riemannian manifolds that admit a Codazzi tensor with two distinct eigenvalues everywhere.

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