# ANNALES DE L'INSTITUT FOURIER

Holomorphic isometries from the Poincaré disk into bounded symmetric domains of rank at least two
Annales de l'Institut Fourier, Volume 69 (2019) no. 5, pp. 2205-2240.

We first study holomorphic isometries from the Poincaré disk into the product of the unit disk and the complex unit $n$-ball for $n\ge 2$. On the other hand, we observe that there exists a holomorphic isometry from the product of the unit disk and the complex unit $n$-ball into any irreducible bounded symmetric domain of rank $\ge 2$ which is not biholomorphic to any type-$\mathrm{IV}$ domain. In particular, our study provides many new examples of holomorphic isometries from the Poincaré disk into irreducible bounded symmetric domains of rank at least $2$ except for type-$\mathrm{IV}$ domains.

Nous étudions d’abord les isométries holomorphes du disque de Poincaré dans le produit du disque unité et de la boule unité complexe $n$-dimensionnelle pour $n\ge 2$. Ensuite, on observe qu’il existe une isométrie holomorphe du produit du disque unité et de la boule unité complexe $n$-dimensionnelle dans tout domaine symétrique borné irréductible de rang $\ge 2$ non-biholomorphe à aucun domaine de type $\mathrm{IV}$. En particulier, notre étude fournit de nombreux nouveaux exemples d’isométries holomorphes du disque de Poincaré dans les domaines symétriques bornés irréductibles de rang au moins deux, à l’exception des domaines de type $\mathrm{IV}$.

Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3293
Classification: 32M15, 53C55, 53C42
Keywords: Holomorphic isometries, Bounded symmetric domains
Chan, Shan Tai 1; Yuan, Yuan 2

1 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
2 Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA
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Chan, Shan Tai; Yuan, Yuan. Holomorphic isometries from the Poincaré disk into bounded symmetric domains of rank at least two. Annales de l'Institut Fourier, Volume 69 (2019) no. 5, pp. 2205-2240. doi : 10.5802/aif.3293. https://aif.centre-mersenne.org/articles/10.5802/aif.3293/

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