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 | References | Similar Articles | Additional Information

Abstract: We prove that any proper holomorphic mapping between two equidimensional irreducible bounded symmetric domains with rank 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

Email:
Tuzhenhan@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06383-3

Keywords:
Bounded symmetric domains,
Hermitian symmetric manifolds,
proper holomorphic mappings,
rigidity,
totally geodesic submanifolds

Received by editor(s):
September 29, 2000

Published electronically:
October 1, 2001

Communicated by:
Steven R. Bell

Article copyright:
© Copyright 2001
American Mathematical Society