Rotational symmetry of complete shrinking gradient Yamabe solitons

2023/09/17 by Shun Maeta, Maeta, Shun · 1 citation
Mathematics · Physics and Astronomy · #53C20 #53C21 #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2309.09166

openalex publication_date 2023/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally symmetric. This assumption is optimal for higher dimensions. This result resolves the Yamabe-soliton analogue of Perelman's conjecture.

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• Complete gradient Einstein-type Sasakian manifolds with α=0

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