STRUCTURE THEOREM FOR COMPACT VAISMAN MANIFOLDS

By L. Ornea, Misha Verbitsky. 2003

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A locally conformally Kahler (l.c.K.) manifold is a complexmanifold admitting a Kahler covering ˜ M, with each deck transformation acting by Kahler homotheties. A compact l.c.K. manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on ˜ M. We prove a structure theorem for compact Vaisman manifolds. Every compact Vaisman manifold M is fibered over a circle, the fibers are Sasakian, the fibration is locally trivial, and M is reconstructed from the Sasakian structure on the fibers and the monodromy automorphism induced by this fibration. This construction is canonical and functorial in both directions.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d027e1d1a530f7b97aeaee0bcac097bc2a7bac90