Year: 2025
Type: preprint
Abstract: We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl tensor and the scalar curvature satisfy a certain sharp pinching condition (closely related, in a precise sense, to that of Kähler metric), then the soliton is necessarily locally Kähler. We further obtain a characterization theorem and a weighted integral gap result for compact gradient shrinking Ricci solitons with bounded modified sectional curvature. In addition, we establish a Hitchin-Thorpe type inequality for compact four-dimensional Ricci solitons, providing new topological constraints on such manifolds.
Source: arXiv (Cornell University)
Authors: Cao, Xiaodong, Ribeiro Jr, Ernani, Wondo, Hosea
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083598935
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