Conformally Einstein-Maxwell Kahler metrics and structure of the automorphism group
Conformally Einstein-Maxwell Kahler metrics and structure of the automorphism group
复制标题
共形爱因斯坦-麦克斯韦卡勒度量和自同构群的结构
DOI：
10.1007/s00209-018-2112-3
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发表时间：
2019
影响因子：
0.8
通讯作者：
Hajime Ono
中科院分区：
文献类型：
--
作者：
Akito Futaki;Hajime Ono
令 (M,g) 为紧凯勒流形和正平滑函数，使得其凯勒哈密顿向量场形成全纯 Killing 向量场。如果共形度量具有恒定的标量曲率，我们就说该对 (g,f) 是共形爱因斯坦-麦克斯韦凯勒度量。在本文中，我们证明了共形爱因斯坦-麦克斯韦凯勒流形全纯矢量场的约简李代数的还原性结果，扩展了恒定标量曲率凯勒流形的利希纳罗维奇-松岛定理。更一般地，我们考虑卡拉比泛函和极值凯勒度量的扩展，并证明卡拉比定理在极值凯勒流形的全纯向量场李代数结构上的扩展。证明在Donaldson-Fujiki 图的设置下使用Hessian 公式计算Calabi 泛函。
Let (M,g) be a compact Kähler manifold andfa positive smooth function such that its Hamiltonian vector fieldfor the Kähler formis a holomorphic Killing vector field. We say that the pair (g,f) is conformally Einstein–Maxwell Kähler metric if the conformal metrichas constant scalar curvature. In this paper we prove a reductiveness result of the reduced Lie algebra of holomorphic vector fields for conformally Einstein–Maxwell Kähler manifolds, extending the Lichnerowicz–Matsushima Theorem for constant scalar curvature Kähler manifolds. More generally we consider extensions of Calabi functional and extremal Kähler metrics, and prove an extension of Calabi’s theorem on the structure of the Lie algebra of holomorphic vector fields for extremal Kähler manifolds. The proof uses a Hessian formula for the Calabi functional under the set up of Donaldson-Fujiki picture.