Weyl-Schouten Theorem for symmetric spaces

Details Weyl-Schouten Theorem for symmetric spaces Weyl-Schouten Theorem for symmetric spaces

2011-07-21

arxiv.org/abs/1107.4260v2

Mathematics

Differential Geometry

Changed some proofs; corrected typos

Scientific paper

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).

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