A Hamiltonian approach to the cohomogeneity one Ricci soliton equations

2014/07/09 by Alejandro Betancourt de la Parra, Andrew Dancer, de la Parra, Alejandro Betancourt +3
Mathematics · Physics and Astronomy · #37J35 #53C25 #53C30 #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.1407.2551

openalex publication_date 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of Kähler type in five dimensions.

Citations

• Painlevé analysis of the Bryant Soliton
• Singular Ricci solitons and their stability under the Ricci flow

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