Griffiths-Harris rigidity of compact Hermitian symmetric spaces

Landsberg, J. M.

J. Differential Geom., Tome 72 (2006) no. 1, p. 395-405 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-11-14
Classification: 32Mxx, 14Jxx

@article{1175266232,
     author = {Landsberg, J. M.},
     title = {Griffiths-Harris rigidity of compact Hermitian symmetric spaces},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 395-405},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175266232}
}

Landsberg, J. M. Griffiths-Harris rigidity of compact Hermitian symmetric spaces. J. Differential Geom., Tome 72 (2006) no. 1, pp.  395-405. http://gdmltest.u-ga.fr/item/1175266232/