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Rigidity of proper holomorphic mappings between equidimensional bounded symmetric domains

Author: Zhen-Han Tu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1035-1042
MSC (2000): Primary 32H02, 32M15
Published electronically: October 1, 2001
MathSciNet review: 1873777
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Abstract: We prove that any proper holomorphic mapping between two equidimensional irreducible bounded symmetric domains with rank $\geq 2$ is a biholomorphism. The proof of the main result in this paper will be achieved by a differential-geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their Bergman metrics.

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Additional Information

Zhen-Han Tu
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Address at time of publication: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China

Keywords: Bounded symmetric domains, Hermitian symmetric manifolds, proper holomorphic mappings, rigidity, totally geodesic submanifolds
Received by editor(s): September 29, 2000
Published electronically: October 1, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society