报告题目：Bergman metrics have constant holomorphic sectional curvatures
时 间：2023年12月12日（星期二）15:00
地 点：理工北楼601
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：In this talk, we study domains in $\mathbf{C}^n$ or Stein manifolds $M$ such that their Bergman metrics have constant holomorphic sectional curvature κ. We discuss the problem in the following three cases.
For κ>0, we first construct an interesting example of domain $\Omega\subset\mathbf{C}^2$ so that its Bergman metric has holomorphic sectional curvature 2. Second, we prove that any complex manifold $M$ of dimension $n$ having positive constant holomorphic sectional curvature is biholomorphic to a domain in $\mathbf{P}^n$ with finite dimensional Bergman space $A^2(M)$.
For κ<0, we prove that every Stein manifold $M$ of dimension $n$ with its Bergman metric has negative constant holomorphic sectional curvature if and only if $M$ is biholomorphic to $B_n \setminus E$, where $B_n$ is the unit ball in $ \mathbf{C}^n$ and $E$ is relatively closed plruipolar set in $B_n$.
For κ=0, we prove that every complex manifold $M$ having a non-constant bounded holomorphic function, can not have flat Bergman metric.
This is joint work with Xiaojun Huang from Rutgers University.
报告人简介：李松鹰(Li Song-Ying), 1992年毕业于美国匹斯堡大学，获博士学位。2004年至今为美国加州大学尔湾分校正教授。李松鹰教授的研究方向为多复变、非线性偏微分方程与复几何，主要涉及了dbar-方程，调和映射的边值问题和刚性问题，算子理论以及Laplacian第一特征值估计等重要问题。在Amer. J. Math., J. Differential Geom., Math. Ann., Adv. Math., J. Funct. Anal., Tran. Amer. Math. Soc., Michigan Math. J., J. London Math. Soc., Anal. PDE, Math. Z., J. Geom. Anal. 等国际一流数学刊物上发表论文数十篇.