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.
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M. S. Baouendi (2005) studied this question.
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