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November 2006 Griffiths-Harris rigidity of compact Hermitian symmetric spaces
J. M. Landsberg
J. Differential Geom. 74(3): 395-405 (November 2006). DOI: 10.4310/jdg/1175266232


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.


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J. M. Landsberg. "Griffiths-Harris rigidity of compact Hermitian symmetric spaces." J. Differential Geom. 74 (3) 395 - 405, November 2006.


Published: November 2006
First available in Project Euclid: 30 March 2007

zbMATH: 1107.53036
MathSciNet: MR2269783
Digital Object Identifier: 10.4310/jdg/1175266232

Primary: 32Mxx
Secondary: 14Jxx

Rights: Copyright © 2006 Lehigh University

Vol.74 • No. 3 • November 2006
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