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Hopf-Rinow Theorem on Convex Complex Finsler Manifolds
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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).
GeodesicDistance functionHopf-Rinow Theorem
LI Hong-jun
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School of Mathematics and Statistics,Henan University,Kaifeng 475004,China
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