Jun 1, 2011
Osaka Journal of Mathematics
By definition, Kahler‐Ricci solitons are defined on Fano mani folds. In this note, we shall generalize the notion of Kahler‐Ricci solitons to the case of general polarized manifolds from the view point of K-energy, which are called “generalized Kahler‐Ricci solitons”. Moreover, “generalized Kahler‐Ricci solitons” are also one of generalizations of constant scalar curvature Kahler metrics. Furthermore, we shall give a non-trivial example of a “generalized Kahler‐Ricci soliton”.