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arXiv · 2105.08284

A Schwarz lemma for weakly K\"ahler-Finsler manifolds

Jun Nie·Chunping Zhong
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Abstract

In this paper, we first establish several theorems about the estimation of distance function on real and strongly convex complex Finsler manifolds and then obtain a Schwarz lemma from a strongly convex weakly K\"ahler-Finsler manifold into a strongly pseudoconvex complex Finsler manifold. As applications, we prove that a holomorphic mapping from a strongly convex weakly K\"ahler-Finsler manifold into a strongly pseudoconvex complex Finsler manifold is necessary constant under an extra condition. In particular, we prove that a holomorphic mapping from a complex Minkowski space into a strongly pseudoconvex complex Finsler manifold such that its holomorphic sectional curvature is bounded from above by a negative constant is necessary constant.

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Jun Nie, Chunping Zhong. 2021-05-18. A Schwarz lemma for weakly K\"ahler-Finsler manifolds. https://doi.org/10.1007/s10231-021-01184-5

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