Connexions affines et projectives sur les surfaces complexes compactes

2008/05/19 by Sorin Dumitrescu, Dumitrescu, Sorin · 1 voice · 1 citation
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.0805.2816

20 pages, french

Abstract

We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection ∇ on a compact complex surface is locally modelled on a translations-invariant affine connection on \C², except if ∇ is a generic connection on a principal elliptic bundle over a Riemann surface of genus g ≥ 2, with odd first Betti number. In the last case, the local Killing Lie algebra is of dimension one, generated by the fundamental vector field of the principal fibration.

Cited by

• Non-Kähler Calabi-Yau manifolds and holomorphic geometric structures

Discussions

• C'est très courant en mathématiques d'utiliser l'adverbe "moralement". Prenez par exemple cet article arxiv.org/pdf/0805.2816 [bsky, 2 points, 3 comments]

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