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

Landsberg, J. M.

J. Differ. Geom. 74, No. 3, 395-405 (2006).

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.

Reviewer: Aurel Bejancu (Safat)

MSC:

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

Keywords:

symmetric space; complex manifold; second fundamental form