Mathematische Zeitschrift

, 264:301 | Cite as

Connexions affines et projectives sur les surfaces complexes compactes

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Résumé

Soit (S, ∇) une surface complexe compacte connexe munie d’une connexion affine holomorphe sans torsion. Nous démontrons que ∇ est localement modelée sur une connexion affine invariante par translations sur C 2 (en particulier, ∇ est localement homogène), sauf si S est un fibré elliptique principal au-dessus d’une surface de genre g ≥ 2, de premier nombre de Betti impair et ∇ est une connexion affine holomorphe sans torsion générique sur S, auquel cas l’algèbre de Lie des champs de Killing locaux est de dimension un, engendrée par le champ fondamental de la fibration principale. Nous en déduisons que toute connexion projective holomorphe normale sur une surface complexe compacte est plate.

Mots clés

Connexions affines holomorphes Connexions projectives holomorphes Surfaces complexes Champs de Killing locaux 

Mathematics Subject Classification (2000)

53B21 53C56 53A55 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.MathématiqueUniversité Paris-Sud (11)Orsay CedexFrance

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