Proceedings of the American Mathematical Society

Rigidity of proper holomorphic mappings between equidimensional bounded symmetric domains

Author(s): Zhen-Han Tu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1035-1042.
MSC (2000): Primary 32H02, 32M15
Posted: October 1, 2001
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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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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
Email: Tuzhenhan@yahoo.com

DOI: 10.1090/S0002-9939-01-06383-3
PII: S 0002-9939(01)06383-3
Keywords: Bounded symmetric domains, Hermitian symmetric manifolds, proper holomorphic mappings, rigidity, totally geodesic submanifolds
Received by editor(s): September 29, 2000
Posted: October 1, 2001
Communicated by: Steven R. Bell
Copyright of article: Copyright 2001, American Mathematical Society

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