Comptes Rendus
no. 6
Differential Geometry
A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in Cn
[Une classe des variétés kählériennes, à courbure non positive, holomorphe à une boule dans Cn]

Présenté par : Étienne Ghys

Harish Seshadri1 ; Kaushal Verma1
1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 427-430.

Soit (M,g) une variété kählérienne complète et simplement connexe à courbure sectionnelle non positive. Supposons que g ait courbure sectionnelle holomorphe constante et négative en delors d'un compact. On démontre que M est biholomorphe à une boule dans Cn, où dimCM=n.

Let (M,g) be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dimCM=n.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.01.005

Harish Seshadri 1 ; Kaushal Verma 1

1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India 
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Harish Seshadri; Kaushal Verma. A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in $ {\mathbb{C}}^{n}$. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 427-430. doi : 10.1016/j.crma.2006.01.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.005/

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