Rotational symmetry of conical Kähler–Ricci solitons

2013/04/10 by Otis Chodosh, Frederick Tsz-Ho Fong
Mathematics · #Conical surface #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Holomorphic function #Infinity #Kähler manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Ricci curvature #Symmetry (geometry) #math.CV #math.DG #msc:35C08 #msc:53C44

paper · pdf · doi:10.1007/s00208-015-1240-x

13 pages; some assumptions removed

arxiv created 2013/04/10 · openalex publication_date 2015/06/05 · arxiv updated 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that expanding Kähler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to Kähler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.

Citations

• The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature
• Ricci flow and the uniformization on complete noncompact Kähler manifolds
• Projective Manifolds with Ample Tangent Bundles
• The formations of singularities in the Ricci Flow
• Constructing Kähler-Ricci solitons from Sasaki-Einstein manifolds
• Compact k�hler manifolds of positive bisectional curvature
• Two-Dimensional Gradient Ricci Solitons Revisited
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Rotational symmetry of self-similar solutions to the Ricci flow