A Rigidity Theorem for the deformed Hermitian-Yang-Mills equation
A Rigidity Theorem for the deformed Hermitian-Yang-Mills equation
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DOI：
10.1007/s00526-020-01880-9
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发表时间：
2021-01
影响因子：
2.1
通讯作者：
Xiaoli Han;Xishen Jin
中科院分区：
文献类型：
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作者：
Xiaoli Han;Xishen Jin
本文研究了紧致Kähler流形上具有非负正交对分曲率的变形Hermitian-Yang-米尔斯方程.证明了当存在一个正的常数C使得$$\开始{aligned} -\frac{1}{C}\omega<\sqrt{-1}F<C\omega时，变形的Hermitian-Yang-米尔斯度量的曲率平行于背景度量.我们还考虑了自收缩流到相应的抛物流的情形。证明了自收缩函数是一个二次多项式函数。最后，我们给出了J-方程和J-流上的自收缩器的一个类似的刚性定理。
In this paper, we study the deformed Hermitian-Yang-Mills equation on compact Kähler manifold with non-negative orthogonal bisectional curvature. We prove that the curvatures of deformed Hermitian-Yang-Mills metrics are parallel with respect to the background metric if there exists a positive constantCsuch that $$\begin{aligned} -\frac{1}{C}\omega<\sqrt{-1}F<C\omega . \end{aligned}$$We also consider the self-shrinker overto the corresponding parabolic flow. We prove that the self-shrinker overis a quadratic polynomial function. At last, we show a similar rigidity theorem for the J-equations and the self-shrinkers overto J-flow.