Three-dimensional Ricci solitons which project to surfaces

2005/10/14 by Paul Baird, Baird, Paul, Laurent Danielo +1 · 4 citations
Mathematics · Physics and Astronomy · #35Q51 #57M50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0510313

openalex publication_date 2005/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study 3-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on the surface. A complete description of the soliton structures on all the 3-dimensional geometries is given, in particular, non-gradient solitons are found on Nil and Sol.

Cited by

• On curvature estimates for four-dimensional gradient Ricci solitons
• Curvature pinching of asymptotically conical gradient expanding Ricci solitons
• A nongradient Ricci almost soliton
• Expanding Ricci solitons and Higgs bundles
• On the long-time behavior of type-III Ricci flow solutions

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