Almost soliton duality

Original · EN

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.