Weyl-Schouten Theorem for symmetric spaces
Differential Geometry
2014-02-26 v2
Abstract
Let N be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W be the Weyl tensor of N at some point. We prove that a Riemannian manifold whose Weyl tensor at every point is a positive multiple of W is conformally equivalent to N (the case N = R^n is the Weyl-Schouten Theorem).
Cite
@article{arxiv.1107.4260,
title = {Weyl-Schouten Theorem for symmetric spaces},
author = {Yuri Nikolayevsky},
journal= {arXiv preprint arXiv:1107.4260},
year = {2014}
}
Comments
Changed some proofs; corrected typos