Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (1): 31-45.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.003

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Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

  

  1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
  • Received:2022-08-31 Online:2024-03-30 Published:2024-03-30
  • Contact: LI Hong-jun (1986-), male, native of Fugou, Henan, assistant professor of Henan University, engages in function theory of several complex variables and complex Finsler geometry. E-mail: lihj@vip.henu.edu.cn
  • About author: LI Hong-jun (1986-), male, native of Fugou, Henan, assistant professor of Henan University, engages in function theory of several complex variables and complex Finsler geometry.
  • Supported by:
     Supported by the National Natural Science Foundation of China (Grant No. 12001165).

Abstract: Suppose (M,F) is a convex complex Finsler manifold. We prove that geodesics
of (M,F) are locally minimizing. Hence, F introduces a distance function d such that
(M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem
holds on (M,F).

Key words:  Geodesic, Distance function, Hopf-Rinow Theorem

CLC Number: