Holomorphic isometries from the Poincar\'e disk into bounded symmetric domains of rank at least two

Shan Tai Chan; Yuan Yuan

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arXiv · 1701.05623

Holomorphic isometries from the Poincar\'e disk into bounded symmetric domains of rank at least two

Shan Tai Chan·Yuan Yuan

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Abstract

We first study holomorphic isometries from the Poincar\'e 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 Poincar\'e disk into irreducible bounded symmetric domains of rank at least $2$ except for type-$\mathrm{IV}$ domains.

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Shan Tai Chan, Yuan Yuan. 2017-01-19. Holomorphic isometries from the Poincar\'e disk into bounded symmetric domains of rank at least two. https://arxiv.org/abs/1701.05623

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