Contact pairs and locally conformally symplectic structures

Abstract

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.

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

References in corpus (3)

• The geometry of symplectic pairs
• Fibrations and fundamental groups of Kaehler-Weyl manifolds
• Stability theorems for symplectic and contact pairs

Cited by in corpus (7)

• Cohomology theories on locally conformal symplectic manifolds
• Bochner and Conformal Flatness of Normal Metric Contact Pairs
• Cohomologies of locally conformally symplectic manifolds and solvmanifolds
• Universal Models via Embedding and Reduction for Locally Conformal Symplectic Structures
• Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics
• Minimality of invariant submanifolds in Metric Contact Pair Geometry
• The convexity package for Hamiltonian actions on conformal symplectic manifolds