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.
"Kähler-Einstein metrics for manifolds with nonvanishing Futaki character." Tohoku Math. J. (2) 53 (2) 171 - 182, 2001. https://doi.org/10.2748/tmj/1178207477