Griffiths-Harris rigidity of compact Hermitian symmetric spaces. (English) Zbl 1107.53036

The author proves that any complex manifold that has a projective second fundamental form isomorphic to one of a rank two compact Hermitian symmetric space (other than a quadric hypersurface) at a general point, must be an open subset of such a space. The calculations are done by using the higher order Bertini theorems.


53C35 Differential geometry of symmetric spaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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