Journal of Differential Geometry

Griffiths-Harris rigidity of compact Hermitian symmetric spaces

J. M. Landsberg

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I prove that any complex manifold that has a projective second fundmental 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. This contrasts the non-rigidity of all other compact Hermitian symmetric spaces observed in J.M. Landsberg and L. Manive's articles. A key step is the use of higher order Bertini type theorems that may be of interest in their own right.

Article information

J. Differential Geom., Volume 74, Number 3 (2006), 395-405.

First available in Project Euclid: 30 March 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Mxx: Complex spaces with a group of automorphisms
Secondary: 14Jxx: Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}


Landsberg, J. M. Griffiths-Harris rigidity of compact Hermitian symmetric spaces. J. Differential Geom. 74 (2006), no. 3, 395--405. doi:10.4310/jdg/1175266232.

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