Cahen-Gutt矩映射,闭Fedosov星积和自同构群的结构

IF 0.6 3区 数学 Q3 MATHEMATICS
A. Futaki, Hajime Ono
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引用次数: 11

摘要

我们证明了如果紧化Kaehler流形$M$允许闭Fedosov星积,则$M$上全纯向量场的约化李代数是约化的。这与La Fuente-Gravy先前发现的阻塞是成对的。更一般地,我们考虑Cahen-Gutt矩映射的平方范数与cscK问题中标量曲率的Calabi泛函相同的精神,并证明了关于极值Kaehler流形全纯向量场李代数结构的Calabi定理的Cahen-Gutt版本。证明使用了Cahen-Gutt矩映射的平方范数的Hessian公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cahen–Gutt moment map, closed Fedosov star product and structure of the automorphism group
We show that if a compact Kaehler manifold $M$ admits closed Fedosov's star product then the reduced Lie algebra of holomorphic vector fields on $M$ is reductive. This comes in pair with the obstruction previously found by La Fuente-Gravy. More generally we consider the squared norm of Cahen-Gutt moment map as in the same spirit of Calabi functional for the scalar curvature in cscK problem, and prove a Cahen-Gutt version of Calabi's theorem on the structure of the Lie algebra of holomorphic vector fields for extremal Kaehler manifolds. The proof uses a Hessian formula for the squared norm of Cahen-Gutt moment map.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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