Schwarz lemma from a K\"ahler manifold into a complex Finsler manifold

Jun Nie; Chunping Zhong

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arXiv · 2105.08720

Schwarz lemma from a K\"ahler manifold into a complex Finsler manifold

Jun Nie·Chunping Zhong

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Abstract

Suppose that $M$ is a K\"ahler manifold with a pole 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 $f$ form $M$ 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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BibTeX RIS

Jun Nie, Chunping Zhong. 2021-05-18. Schwarz lemma from a K\"ahler manifold into a complex Finsler manifold. https://arxiv.org/abs/2105.08720

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