We study local holomorphic mappings sending a piece of a real hyperquadric in a complex space into a hyperquadric in another complex space of possibly larger dimension. We show that these mappings possess strong super-rigidity properties when the hyperquadrics have positive signatures. These results are applied in the context of holomorphic mappings between classical domains in complex projective spaces of different dimensions.
"Super-rigidity for Holomorphic Mappings between Hyperquadrics with Positive Signature." J. Differential Geom. 69 (2) 379 - 398, Feb 2005. https://doi.org/10.4310/jdg/1121449110