On U(n)-invariant strongly convex complex Finsler metrics

• 作者: Kun Wang Hongchuan Xia Chunping Zhong
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（11）
• 所属期刊栏目: Articles
• 页码范围: 2461-2478
• 页数: 18页
• 语种: 英文

摘要

In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in Cn to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable examples.We prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian metric.We give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler metric.Finally,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S2n-1 C Cn share a specific property as that of the complex Wrona metric on Cn.