Connexions affines et projectives sur les surfaces complexes compactes

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dc.creatorDumitrescu, Sorin
dc.date2008-05-19
dc.date.accessioned2026-07-07T09:39:41Z
dc.date.available2026-07-07T09:39:41Z
dc.descriptionWe prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection $\nabla$ on a compact complex surface is locally modelled on a translations-invariant affine connection on $\C^2$, except if $\nabla$ is a generic connection on a principal elliptic bundle over a Riemann surface of genus $g \geq 2$, 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.
dc.description20 pages, french
dc.identifierhttps://arxiv.org/abs/0805.2816
dc.identifierhttp://arxiv.org/abs/0805.2816
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161264
dc.subjectDifferential Geometry
dc.subjectComplex Variables
dc.subject53B21;53C56;53A55
dc.titleConnexions affines et projectives sur les surfaces complexes compactes
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