Conformal de Rham decomposition of Riemannian manifolds

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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.
17 pages

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Differential Geometry, 53B25

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http://salesiana.dossiersoluciones.com/handle/123456789/70954

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404434
 http://arxiv.org/abs/math/0404434

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arXiv