2003/06/22 by L. Ornea, M. Verbitsky
Mathematics · #math.AG #math.CV #math.DG #msc:53C55 #msc:14E25 #msc:53C25
published as Math. Ann. 332 (2005), no. 1, 121--143. · 28 pages. A reference added
arxiv created 2003/06/22 · arxiv updated 2009/11/30
A locally conformally Kaehler (LCK) manifold is a complex manifold admitting a Kaehler covering M, with monodromy acting on M by Kaehler homotheties. A compact LCK manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on M. We prove a non-Kaehler analogue of Kodaira embedding theorem: any compact Vaisman manifold admits a natural holomorphic immersion to a Hopf manifold. As an application, we obtain that any Sasakian manifold has a contact immersion to an odd-dimensional sphere.