Schwarz lemma on bounded symmetric domains endowed with holomorphic invariant Kähler--Berwald metrics

Yong He; Chunping Zhong

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arXiv · 2609.34435

Schwarz lemma on bounded symmetric domains endowed with holomorphic invariant Kähler--Berwald metrics

Yong He·Chunping Zhong

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Abstract

We prove a rigidity theorem: a globally symmetric complex Finsler space $(M, J, F)$ is necessarily a Kähler-Berwald space, namely $F$ must be a Kähler-Berwald metric. We also obtain a Schwarz lemma for holomorphic mappings $f$ from an arbitrary bounded symmetric domain $\mathfrak{D}$ into itself whenever $\mathfrak{D}$ is endowed with an $\mbox{Aut}(\mathfrak{D})$-invariant Kähler-Berwald metric $F$ such that its holomorphic sectional curvature is bounded below and above by negative constants $-K_1<0$ and $-K_2<0$, respectively. The novelty of this Schwarz lemma is that the Lu constant of $(\mathfrak{D},F)$ is optimal for each given $F$ whenever rank$(\mathfrak{D})\geq 2$.

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BibTeX RIS

Yong He, Chunping Zhong. 2026-09-28. Schwarz lemma on bounded symmetric domains endowed with holomorphic invariant Kähler--Berwald metrics. https://arxiv.org/abs/2609.34435

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