A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in $ {\mathbb{C}}^{n}$

Harish Seshadri; Kaushal Verma

doi:10.1016/j.crma.2006.01.005

Differential Geometry

A class of nonpositively curved Kähler manifolds biholomorphic to the unit ball in

C^{n}

Presented by: Étienne Ghys

Harish Seshadri ¹; Kaushal Verma ¹

¹ Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 427-430.

Abstract
Résumé

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 $C^{n}$ , where $\dim_{C} M = n$ .

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 $C^{n}$ , où $\dim_{C} M = n$ .

Received: 2005-11-13
Accepted: 2005-12-20
Published online: 2006-01-27

DOI: 10.1016/j.crma.2006.01.005

Author's affiliations:

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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