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Immersion theorem for Vaisman manifolds

L. Ornea·M. Verbitsky
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Abstract

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.

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L. Ornea, M. Verbitsky. 2003-06-22. Immersion theorem for Vaisman manifolds. https://arxiv.org/abs/math/0306077

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