Mathematical Research Letters
Volume 19 (2012)
Cycle spaces of flag domains on Grassmannians and rigidity of holomorphic mappings
Pages: 1219 – 1236
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.