On steady and expanding Ricci solitons with asymptotic symmetries

2025/05/26 by Michael B. Law, Law, Michael B.
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2505.20576

Abstract

We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.

Citations

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• Rotational symmetry of Ricci solitons in higher dimensions
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• The entropy formula for the Ricci flow and its geometric applications

Related

• Uniqueness of gradient Ricci solitons
• Rigidity of positively curved Steady gradient Ricci solitons on orbifolds
• 4d steady gradient Ricci solitons with nonnegative curvature away from a compact set
• Unique Asymptotics of Steady Ricci Solitons with Symmetry
• On Four-dimensional Steady gradient Ricci solitons that dimension reduce