H-functional and Matsushima type decomposition theorem

Abstract

The H-functional characterizes K\"ahler-Ricci solitons as its critical points, and also plays an important role of the existence problem for K\"ahler-Einstein metrics. In this paper we prove the Hessian formula for the H-functional at its critical points, and use this to obtain a new proof of Matsushima type decomposition theorem for holomorphic vector fields on Fano manifolds admitting K\"ahler-Ricci solitons.Comment: Typos are fixed. References are adde