Abstract
We prove that any n-dimensional complete gradient shrinking Ricci soliton with pinched Weyl curvature is a finite quotient of \({\mathbb{R}^{n}, \mathbb{R}\times \mathbb{S}^{n-1}}\) or \({\mathbb{S}^{n}}\) . In particular, we do not need to assume the metric to be locally conformally flat.
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Catino, G. Complete gradient shrinking Ricci solitons with pinched curvature. Math. Ann. 355, 629–635 (2013). https://doi.org/10.1007/s00208-012-0800-6
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DOI: https://doi.org/10.1007/s00208-012-0800-6