Immersion theorem for Vaisman manifolds

Details Immersion theorem for Vaisman manifolds Immersion theorem for Vaisman manifolds

2003-06-04

arxiv.org/abs/math/0306077v3

Math. Ann. 332 (2005), no. 1, 121--143.

Mathematics

Algebraic Geometry

28 pages. A reference added

Scientific paper

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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