Contact pairs and locally conformally symplectic structures

Details Contact pairs and locally conformally symplectic structures Contact pairs and locally conformally symplectic structures

2010-06-02

arxiv.org/abs/1006.0315v2

pp. 85--98 in Harmonic maps and differential geometry, Contemp. Math., 542, Amer. Math. Soc., Providence, RI, 2011

Mathematics

Symplectic Geometry

13 pages; corrected two misprints; to appear in Contemporary Mathematics

Scientific paper

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is endowed with a normal metric, then the corresponding lcs form is locally conformally Kaehler, and, in fact, Vaisman. This leads to classification results for normal metric contact pairs. In complex dimension two we obtain a new proof of Belgun's classification of Vaisman manifolds under the additional assumption that the Kodaira dimension is non-negative. We also produce many examples of manifolds admitting locally conformally symplectic structures but no locally conformally Kaehler ones.

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