Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

LI Hong-jun

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

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 1: 31 - 45

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.01.003

Hopf-Rinow Theorem on Convex Complex Finsler Manifolds

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

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.

Received date: 2022-08-31

Online published: 2024-03-30

Supported by

Supported by the National Natural Science Foundation of China (Grant No. 12001165).

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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

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LI Hong-jun . Hopf-Rinow Theorem on Convex Complex Finsler Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(1) : 31 -45 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.003

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