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Schwarz lemma from a Kähler manifold into a complex Finsler manifold

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Abstract

Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below. Suppose that N is a strongly pseudoconvex complex Finsler manifold such that its holomorphic sectional curvature is bounded from above by a negative constant. In this paper, we establish a Schwarz lemma for holomorphic mappings f from M into N. As applications, we obtain a Liouville type rigidity result for holomorphic mappings f from M into N, as well as a rigidity theorem for bimeromorphic mappings from a compact complex manifold into a compact complex Finsler manifold.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12071386, 11671330 and 11971401). The authors thank the referees for carefully reading the manuscript and their helpful corrections/suggestions which improved the presentation of the paper.

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Authors and Affiliations

  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. Schwarz lemma from a Kähler manifold into a complex Finsler manifold. Sci. China Math. 65, 1661–1678 (2022). https://doi.org/10.1007/s11425-021-1878-9

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  • DOI: https://doi.org/10.1007/s11425-021-1878-9

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