English

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).

Keywords

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

R2 v1 2026-06-21T18:40:02.347Z