Schwarz lemma on bounded symmetric domains endowed with holomorphic invariant Kähler--Berwald metrics
Year: 2026
Type: preprint
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$(\mathfrak{D})\geq 2$.
Source: arXiv (Cornell University)
Authors: He, Yong, Zhong, Chunping
Institutions: Xinjiang Normal University, Xiamen University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3237435281, G8809743928
OpenAlex ID: W7214718034