On the Complex Structure of Kähler Manifolds with Nonnegative Curvature

Chau, Albert; Tam, Luen-Fai

J. Differential Geom., Tome 72 (2006) no. 1, p. 491-530 / Harvested from Project Euclid

Résumé

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative and bounded holomorphic bi-sectional curvature and maximal volume growth is biholomorphic to complex Euclidean space Cⁿ. We also show that the volume growth condition can be removed if we assume the Kähler manifold has average quadratic scalar curvature decay and positive curvature operator.

Publié le : 2006-06-14
Classification:

@article{1146169936,
     author = {Chau, Albert and Tam, Luen-Fai},
     title = {On the Complex Structure of K\"ahler Manifolds with Nonnegative Curvature},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 491-530},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1146169936}
}

Chau, Albert; Tam, Luen-Fai. On the Complex Structure of Kähler Manifolds with Nonnegative Curvature. J. Differential Geom., Tome 72 (2006) no. 1, pp.  491-530. http://gdmltest.u-ga.fr/item/1146169936/