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Rigidity of four-dimensional K\"ahler-Ricci solitons
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abstract
In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\"ahler model. The first theorem could be considered as a rigidity result for the K\"ahler-Ricci soliton structure on $\mathbb{S}^2\times \mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a K\"ahler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally K\"ahler.
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Cited by 1 Pith paper
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Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
Under sharp pinching conditions on the self-dual Weyl tensor, scalar curvature, and modified sectional curvature, four-dimensional gradient shrinking Ricci solitons are forced to be locally Kähler, isometric to S^4 or...
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