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}

[Une classe des variétés kählériennes, à courbure non positive, holomorphe à une boule dans

C^{n}

]

Présenté par : 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.

Résumé
Abstract

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 $\dim_{C} M = n$ .

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 $\dim_{C} M = n$ .

Reçu le : 2005-11-13
Accepté le : 2005-12-20
Publié le : 2006-01-27

DOI : 10.1016/j.crma.2006.01.005

Affiliations des auteurs :

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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Bingyuan Liu On the manifolds with noncompact automorphism groups, Complex Analysis and Operator Theory, Volume 18 (2024) no. 8, p. 8 (Id/No 172) | DOI:10.1007/s11785-024-01601-6 | Zbl:7946693
Hervé Gaussier; Andrew Zimmer A metric analogue of Hartogs' theorem, Geometric and Functional Analysis. GAFA, Volume 32 (2022) no. 5, pp. 1041-1062 | DOI:10.1007/s00039-022-00615-6 | Zbl:1515.32004
Si-En Gong; Hongyi Liu; Bin Xu Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature, Proceedings of the American Mathematical Society, Volume 148 (2020) no. 5, pp. 2179-2191 | DOI:10.1090/proc/14835 | Zbl:1445.53016

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