On Locally Conformally Flat Gradient Shrinking Ricci Solitons

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In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence of this identity, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.
13 pages, revised version, third author added

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Differential Geometry, 53C25, 53C44

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http://salesiana.dossiersoluciones.com/handle/123456789/173825

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.0588
 http://arxiv.org/abs/0807.0588

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arXiv