Rotational symmetry of Ricci solitons in higher dimensions

2012/03/01 by Simon Brendle, Brendle, S. · 5 citations
Mathematics · Physics and Astronomy · #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.1203.0270

openalex publication_date 2012/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a steady gradient Ricci soliton of dimension n ≥ 4 which has positive sectional curvature and is asymptotically cylindrical. Under these assumptions, we show that (M,g) is rotationally symmetric. In particular, our result applies to steady gradient Ricci solitons in dimension 4 which are κ-noncollapsed and have positive isotropic curvature.

Cited by

• Curvature estimates for steady and expanding solitons in higher dimensions
• On type-II singularities in Ricci flow on ℝ^N
• Curvature pinching of asymptotically conical gradient expanding Ricci solitons
• Rigidity of Five-Dimensional shrinking gradient Ricci solitons
• On steady and expanding Ricci solitons with asymptotic symmetries

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