On proper holomorphic mappings among irreducible bounded symmetric domains of rank at least $2$
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- by Sui-Chung Ng
- Proc. Amer. Math. Soc. 143 (2015), 219-225
- DOI: https://doi.org/10.1090/S0002-9939-2014-12226-X
- Published electronically: September 15, 2014
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Abstract:
We give a characterization for totally geodesic embeddings between higher-rank irreducible bounded symmetric domains in terms of certain totally geodesic rank-1 symmetric subspaces. More explicitly, we prove that for two irreducible bounded symmetric domains $\Omega _1,\Omega _2$ of rank at least 2, a holomorphic map $F:\Omega _1\rightarrow \Omega _2$ is a totally geodesic embedding with respect to the Bergman metrics if $F$ maps the minimal disks of $\Omega _1$ into rank-1 characteristic symmetric subspaces of $\Omega _2$. As a simple corollary, we obtain a much simpler proof for a theorem of Tsai which says that $F$ is totally geodesic if $F$ is proper and $\operatorname {rank}(\Omega _1) = \operatorname {rank}(\Omega _2)$.References
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Bibliographic Information
- Sui-Chung Ng
- Affiliation: Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, Pennsylvania 19122
- Email: scng@temple.edu
- Received by editor(s): October 15, 2012
- Received by editor(s) in revised form: March 20, 2013
- Published electronically: September 15, 2014
- Communicated by: Franc Forstneric
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 219-225
- MSC (2010): Primary 32H35, 32M15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12226-X
- MathSciNet review: 3272747