Rigidity of four-dimensional Kähler-Ricci solitons
Abstract
In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a Kähler model. The first theorem could be considered as a rigidity result for the Kähler-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 the norm of the self-dual Weyl tensor and the scalar curvature is close to that on a Kähler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally Kähler.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Volume
- 34
- Issue
- 1
- Pages
- 89–114
- Publication date
- 1 January 2026
- Language
- EN