On generalized Kähler--Ricci solitons

Abstract

By definition, Kähler--Ricci solitons are defined on Fano manifolds. In this note, we shall generalize the notion of Kähler--Ricci solitons to the case of general polarized manifolds from the view point of K-energy, which are called ``generalized Kähler--Ricci solitons''. Moreover, ``generalized Kähler--Ricci solitons'' are also one of generalizations of constant scalar curvature Kähler metrics. Furthermore, we shall give a non-trivial example of a ``generalized Kähler--Ricci soliton''.