no. 5
Holomorphic isometries from the Poincaré disk into bounded symmetric domains of rank at least two
[Isométries holomorphes du disque de Poincaré dans les domaines symétriques bornés de rang au moins deux]
Chan, Shan Tai1 ; Yuan, Yuan2
1 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
2 Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA
Annales de l'Institut Fourier, Tome 69 (2019) no. 5, pp. 2205-2240.

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≥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 ≥2 non-biholomorphe à aucun domaine de type 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 IV.

We first study holomorphic isometries from the Poincaré disk into the product of the unit disk and the complex unit n-ball for n≥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 ≥2 which is not biholomorphic to any type-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-IV domains.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3293
Classification : 32M15, 53C55, 53C42
Keywords: Holomorphic isometries, Bounded symmetric domains
Mot clés : isométries holomorphes, domaines symétriques bornés

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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 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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