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A Schwarz lemma for weakly Kähler-Finsler manifolds

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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 Kähler-Finsler manifold into a strongly pseudoconvex complex Finsler manifold. As applications, we prove that a holomorphic mapping from a strongly convex weakly Kähler-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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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12071386, No. 11671330, No. 11271304, No. 11971401).

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  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Jun Nie & Chunping Zhong

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  1. Jun Nie
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  2. Chunping Zhong
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Correspondence to Chunping Zhong.

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Nie, J., Zhong, C. A Schwarz lemma for weakly Kähler-Finsler manifolds. Annali di Matematica 201, 1935–1964 (2022). https://doi.org/10.1007/s10231-021-01184-5

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