  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.
