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Mathematische Annalen

, 345:53 | Cite as

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

  • Sorin DumitrescuEmail author
  • Abdelghani Zeghib
Article

Abstract

We study compact complex 3-manifolds M admitting a (locally homogeneous) holomorphic Riemannian metric g. We prove the following: (i) If the Killing Lie algebra of g has a non trivial semi-simple part, then it preserves some holomorphic Riemannian metric on M with constant sectional curvature; (ii) If the Killing Lie algebra of g is solvable, then, up to a finite unramified cover, M is a quotient Γ\G, where Γ is a lattice in G and G is either the complex Heisenberg group, or the complex SOL group.

Mathematics Subject Classification (2000)

53B21 53C56 53A55 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Département de Mathématiques d’Orsay, équipe de Topologie et Dynamique, Bat. 425, UMR 8628 CNRSUniv. Paris-Sud (11)Orsay CedexFrance
  2. 2.CNRS, UMPA, école Normale Supérieure de LyonLyon Cedex 07France

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