Global rigidity of holomorphic Riemannian metrics on compact complex 3-manifolds

2007/10/24 by Sorin Dumitrescu, Dumitrescu, Sorin, Abdelghani Zeghib +1
Mathematics · #53A55 #53B21 #53C56 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:53A55 #msc:53B21 #msc:53C56

paper · pdf · doi:10.48550/arxiv.0710.4492

28 pages

arxiv created 2007/10/24 · arxiv updated 2009/12/01

Abstract

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

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