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arXiv:1107.4260 [math.DG]AbstractReferencesReviewsResources

Weyl-Schouten Theorem for symmetric spaces

Yuri Nikolayevsky

Published 2011-07-21, updated 2012-02-22Version 2

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).

Comments: Changed some proofs; corrected typos
Categories: math.DG
Subjects: 53A30, 53C35, 53B20
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