Conformal de Rham decomposition of Riemannian manifolds

Ruy Tojeiro

Conformal de Rham decomposition of Riemannian manifolds

Differential Geometry 2007-05-23 v1

Authors: Ruy Tojeiro

Abstract

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.

Keywords

Riemannian manifolds conformal de Rham decomposition warped product Codazzi tensor local decomposition

Cite

@article{arxiv.math/0404434,
  title  = {Conformal de Rham decomposition of Riemannian manifolds},
  author = {Ruy Tojeiro},
  journal= {arXiv preprint arXiv:math/0404434},
  year   = {2007}
}

Comments

17 pages

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