Holomorphic invariant strongly pseudoconvex complex Finsler metrics on the irreducible classical domains

讲座时间 Datetime: 2022年9月24日，星期六，14:30-15:30

地点 Venue: 腾讯线上会议：919-470-572

主持人 Host：邵国宽

报告人 Speaker: 钟春平 

单位 Affiliation: 厦门大学

报告摘要 Abstract:

In this talk, I will show that the unit ball $B_n\subset\mathbb{C}^n$ admits no $\mbox{Aut}(B_n)$-invariant strongly pseudoconvex complex Finsler metric other than a constant multiple of the Poincar$\acute{\mbox{e}}$-Bergman metric, while the unit polydisc $P_n\subset\mathbb{C}^n(n\geq 2)$ admits infinite many $\mbox{Aut}(P_n)$-invariant strongly convex complex Finsler metrics other than the Bergman metric.

We also give an explicit construction of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the irreducible classical domains of type $I-IV$ with rank $\geq 2$. The metrics constructed by us are all K\"ahler-Berwald metrics with negative holomorphic sectional curvatures and nonpositive holomorphic bisectional curvatures.