KÄHLER-EINSTEIN METRICS FOR MANIFOLDS WITH NONVANISHING FUTAKI CHARACTER

Abstract

In this paper, we generalize the concept of Kähler-Einstein metrics for Fano manifolds with nonvanishing Futaki character. Similar to Kähler-Einstein metrics, these new metrics have various nice properties. In addition, the equations for the metrics are in general neither those of extremal Kähler metrics nor those of Kähler-Ricci solitons.