Almost soliton duality

2013/01/02 by Gideon Maschler, Maschler, Gideon · 2 citations
Mathematics · Physics and Astronomy · #53C25 (Primary) 53C55 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1301.0290

openalex publication_date 2013/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gradient Ricci almost solitons were introduced by Pigola, Rigoli, Rimoldi and Setti. They are defined as solitons except that the metric coefficient is required to be a smooth function rather than a constant. It is shown that any almost soliton is conformal to another almost soliton having a soliton function which is minus the original one. Uniqueness, and the case where both the source and target are solitons, are studied. Completeness of the target metric is also examined in the case where the source is Kähler and admits a special Kähler-Ricci potential in the sense given by Derdzinski and Maschler.

Citations

• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Ricci solitons: the equation point of view

Cited by

• Local Structure of Gradient Almost Ricci Solitons with Harmonic Weyl Tensor
• Topology at infinity of complete gradient Schouten solitons

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