Remarks on holomorphic isometric embeddings between bounded symmetric domains
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In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.
KeywordsHolomorphic isometries Bergman kernels Bounded symmetric domains
Mathematics Subject ClassificationPrimary 53C55 32H02 32M15
The main part of this work was done during the summer of 2017 when the author visited The University of Hong Kong and was a postdoctoral fellow at Syracuse University. The author would like to express his gratitude to Professors Ngaiming Mok and Wing-Keung To for helpful discussions on the topic of holomorphic isometric embeddings between (reducible) bounded symmetric domains.
- 3.Mok, N.: Metric rigidity theorems on Hermitian locally symmetric manifolds, Series in Pure Mathematics, vol. 6, World Scientific Publishing Co., Singapore; Teaneck, NJ (1989)Google Scholar
- 6.Xiao, M., Yuan, Y.: Holomorphic maps from the complex unit ball to Type \(\rm IV\) classical domains, arXiv:1606.04806
- 11.Chan, S.-T.: On holomorphic isometric embeddings of complex unit balls into bounded symmetric domains, Ph.D. thesis at The University of Hong Kong (2016)Google Scholar
- 13.Chan, S.-T., Yuan, Y.: Holomorphic isometries from the Poincare disk into bounded symmetric domains of rank at least two, arXiv:1701.05623
- 16.Upmeier, H., Wang, K., Zhang, G.: Holomorphic isometries from the unit ball into symmetric domains. Int. Math. Res. Not. 2019, 55–89 (2017)Google Scholar
- 18.Loos, O.: Bounded symmetric domains and Jordan pairs, Math. Univ. of California, Irvine, Lectures (1977)Google Scholar
- 19.Wolf, J.A.: Fine structures of Hermitian symmetric spaces, Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), pp. 271–357. Pure and App. Math., vol. 8. Dekker, New York (1972)Google Scholar
- 21.Mok, N.: Ergodicity, bounded holomorphic functions and geometric structures in rigidity results on bounded symmetric domains. In: Proceedings of the International Congress of Chinese Mathematicians (Hangzhou 2007), vol 2, pp. 464–505. Higher Educational Press, Beijing (2007)Google Scholar