2020/05/20 by Kun Wang, Wang, Kun, Hongchuan Xia +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #53C40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fibroblast Growth Factor Research #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2005.10022
openalex publication_date 2020/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 relationship between real and complex Finsler geometry 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 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 \pmbS2n-1⊂ℂn share a specific property as that of the complex Wrona metric on ℂn.cc