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

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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Published 18 July 2013