凸复Finsler流形上的Hopf-Rinow定理

doi:10.13371/j.cnki.chin.q.j.m.2024.01.003

数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 31-45.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.003

凸复Finsler流形上的Hopf-Rinow定理

李鸿军

School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

收稿日期:2022-08-31 出版日期:2024-03-30 发布日期:2024-03-30
通讯作者: 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
作者简介: 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.
基金资助:
Supported by the National Natural Science Foundation of China (Grant No. 12001165).

Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

LI Hong-jun

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).

摘要/Abstract

摘要： 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).

关键词: Geodesic, Distance function, Hopf-Rinow Theorem

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

中图分类号:

O187.1

李鸿军. 凸复Finsler流形上的Hopf-Rinow定理[J]. 数学季刊, 2024, 39(1): 31-45.

LI Hong-jun. Hopf-Rinow Theorem on Convex Complex Finsler Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 31-45.

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凸复Finsler流形上的Hopf-Rinow定理

Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

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