Mathematische Annalen

, Volume 332, Issue 1, pp 121–143 | Cite as

An immersion theorem for Vaisman manifolds

  • Liviu Ornea
  • Misha VerbitskyEmail author


A locally conformally Kähler (LCK) manifold is a complex manifold admitting a Kähler covering Open image in new window , with monodromy acting on Open image in new window by Kähler homotheties. A compact LCK manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on Open image in new window . We prove that any compact Vaisman manifold admits a natural holomorphic immersion to a Hopf manifold (ℂ n ∖0)ℤ. As an application, we obtain that any Sasakian manifold has a contact immersion to an odd-dimensional sphere.


Manifold Complex Manifold Hopf Manifold Holomorphic Immersion Vaisman Manifold 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania
  2. 2.Department of MathematicsUniversity of GlasgowGlasgowScotland

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