On proper holomorphic maps between bounded symmetric domains

DOI10.1090/proc/14657zbMath1444.32020arXiv1904.04477OpenAlexW2949674107MaRDI QIDQ5206198

Shan Tai Chan

Publication date: 18 December 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.04477

zbMATH Keywords

proper holomorphic mapbounded symmetric domainstotally geodesic isometric embedding

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• Rigidity for local holomorphic isometric embeddings from \(\mathbb{B}^n\) into \(\mathbb{B}^{N_1} \times \cdots \times \mathbb{B}^{N_m}\) up to conformal factors
• Rigidity of proper holomorphic maps between symmetric domains
• Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric
• Remarks on holomorphic isometric embeddings between bounded symmetric domains
• Proper holomorphic maps between balls of different dimensions
• Remark on proper holomorphic maps between reducible bounded symmetric domains
• Holomorphic isometries of the complex unit ball into irreducible bounded symmetric domains
• Holomorphic isometries between products of complex unit balls
• On proper holomorphic mappings among irreducible bounded symmetric domains of rank at least $2$

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