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1On U(n)-invariant strongly convex complex Finsler metrics显示文摘In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) 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 S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n).Kun Wang Hongchuan Xia Chunping Zhong 2021Science China Mathematics2021,64,11:1
2A REMARK ON GENERAL COMPLEX(α,β)METRICS显示文摘In this paper,we give a characterization for the general complex(α,β)metrics to be strongly convex.As an application,we show that the well-known complex Randers metrics are strongly convex complex Finsler metrics,whereas the complex Kropina metrics are only strongly pseudoconvex.夏红川 钟春平 2021Acta Mathematica Scientia2021,41,3:0
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