Comptes Rendus
no. 6
Algebraic Geometry/Differential Geometry
Kähler manifolds with numerically effective Ricci class and maximal first Betti number are tori
Jean-Pierre Demailly
Fuquan Fang1, 2
1Department of Mathematics, Capital Normal University, Beijing 100037, PR China
2Chern Institute of Mathematics, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 411-416

Let M be a n-dimensional Kähler manifold with numerically effective Ricci class c1(M). In this Note we prove that, if the first Betti number b1(M) is equal to 2n, then M is biholomorphic to a n-dimensional complex torus.

Soit M une variété kählérienne compacte de dimension n et de classe de Ricci c1(M) numériquement effective. Dans cette note nous montrons que si le premier nombre de Betti b1(M) est égal à 2n, alors M est biholomorphe à un tore complexe de dimension n.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.11.019

Fuquan Fang  1 , 2

1 Department of Mathematics, Capital Normal University, Beijing 100037, PR China
2 Chern Institute of Mathematics, Nankai University, Tianjin 300071, PR China 
Fuquan Fang. Kähler manifolds with numerically effective Ricci class and maximal first Betti number are tori. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 411-416. doi: 10.1016/j.crma.2005.11.019
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