On normal contact pairs

TL;DR

This paper studies manifolds with contact pair structures, introduces the concept of normal contact pairs with integrable associated structures, and generalizes a theorem to construct new complex manifolds via flat bundles and Boothby--Wang fibrations.

Contribution

It generalizes Morimoto's theorem to flat bundles and provides new methods for constructing complex manifolds from contact-symplectic bases.

Findings

Generalization of Morimoto's theorem to flat bundles

Construction of examples on Boothby--Wang fibrations

New methods for creating complex manifolds

Abstract

We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto's Theorem on product of almost contact manifolds to flat bundles. We construct some examples on Boothby--Wang fibrations over contact-symplectic manifolds. In particular, these results give new methods to construct complex manifolds.