Mathematical Research Letters

Volume 19 (2012)

Number 6

Cycle spaces of flag domains on Grassmannians and rigidity of holomorphic mappings

Pages: 1219 – 1236

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n6.a4

Author

Sui-Chung Ng (Department of Mathematics, The University of Hong Kong)

Abstract

We study certain cycle spaces on flag domains of $SU(p, q)$-type on Grassmannians and their relations with the rigidity of holomorphic mappings between Grassmannians. Rigidity is obtained for those holomorphic maps that preserve the distinguished boundaries of these flag domains. Our results cover in particular certain special cases of Baouendi-Huang’s Theorem on local proper holomorphic mappings between generalized balls of equal signature.

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