关于具有全纯不变Kähler--Berwald度量的有界对称域上的Schwarz引理
Schwarz lemma on bounded symmetric domains endowed with holomorphic invariant Kähler--Berwald metrics
- Xinjiang Normal University（新疆师范大学）
- Xiamen University（厦门大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明全局对称复Finsler空间必为Kähler-Berwald空间，并给出有界对称域上带不变Kähler-Berwald度量的Schwarz引理，其Lu常数在秩≥2时最优。
AI中文摘要：
我们证明了一个刚性定理：一个全局对称的复Finsler空间$(M, J, F)$必然是Kähler-Berwald空间，即$F$必须是Kähler-Berwald度量。我们还得到了一个Schwarz引理，适用于从任意有界对称域$\mathfrak{D}$到自身的全纯映射$f$，只要$\mathfrak{D}$配备了一个$\mbox{Aut}(\mathfrak{D})$-不变的Kähler-Berwald度量$F$，且其全纯截面曲率分别被负常数$-K_1<0$和$-K_2<0$从下方和上方界定。此Schwarz引理的新颖之处在于，当rank$(\mathfrak{D})\geq 2$时，对于每个给定的$F$，$(\mathfrak{D},F)$的Lu常数是最优的。
英文摘要：
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$(\mathfrak{D})\geq 2$.
