Hessian of the Ricci Calabi functional
Hessian of the Ricci Calabi functional
复制标题
Ricci Calabi 泛函的 Hessian 矩阵
DOI：
10.1090/proc/14321
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发表时间：
2019
影响因子：
1
通讯作者：
Satoshi Nakamura
中科院分区：
文献类型：
--
作者：
Ozawa;I.;& Yuzawa;M;小澤郁美・湯澤正通;小澤郁美・湯澤正通;小澤郁美・湯澤正通;Satoshi Nakamura
Ricci-Calabi泛函是Fano流形的Kähler度量空间上的泛函。它的临界点被称为广义Kähler-Einstein度量。本文证明了Ricci-Calabi泛函的Hessian在广义Kähler-Einstein度量下是非负的.作为其应用，我们给出了全纯向量场的Matsushima型分解定理的另一个证明，该定理最初由Mabuchi证明。本文还讨论了与Collins-Hisamoto-Takahashi最近提出的逆Monge-Ampère流的关系。引用
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. References