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]
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 n2. 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 n2. 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.

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DOI : https://doi.org/10.5802/aif.3293
Classification : 32M15,  53C55,  53C42
Mots clés : isométries holomorphes, domaines symétriques bornés
@article{AIF_2019__69_5_2205_0,
     author = {Chan, Shan Tai and Yuan, Yuan},
     title = {Holomorphic isometries from the Poincar\'e disk into bounded symmetric domains of rank at least two},
     journal = {Annales de l'Institut Fourier},
     pages = {2205--2240},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {5},
     year = {2019},
     doi = {10.5802/aif.3293},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3293/}
}
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. http://archive.numdam.org/articles/10.5802/aif.3293/

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