Hessian of the Ricci-Calabi functional

Nakamura, Satoshi

doi:10.1090/proc/14321

Hessian of the Ricci-Calabi functional
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Proc. Amer. Math. Soc. 147 (2019), 1247-1254 Request permission

Abstract:

The Ricci-Calabi functional is a functional on the space of Kähler metrics of Fano manifolds. Its critical points are called generalized Kähler-Einstein metrics. In this article, we show that the Hessian of the Ricci-Calabi functional is non-negative at generalized Kähler-Einstein metrics. As its application, we give another proof of a Matsushima type decomposition theorem for holomorphic vector fields, which was originally proved by Mabuchi. We also discuss a relation to the inverse Monge-Ampère flow developed recently by Collins-Hisamoto-Takahashi.

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