A Boothby-Wang construction in generalized contact geometry

TL;DR

This paper extends the Boothby-Wang theorem to generalized contact geometry, introduces new construction methods for generalized contact structures, and explores their properties and examples using Courant reduction.

Contribution

It provides a generalized Boothby-Wang theorem, a method for constructing diverse generalized contact structures, and insights into their geometric properties via Courant reduction.

Findings

Established a generalized Boothby-Wang theorem.

Developed a method for constructing non-Poon-Wade type structures.

Constructed generalized complex structures on leaf spaces.

Abstract

We establish a generalized analogue of the Boothby-Wang theorem in generalized contact geometry, along with related results. We present a general method for constructing examples of generalized contact structures that are not of Poon-Wade type, and even examples that fail to be generalized contact structures. Using Courant reduction methods, we construct a generalized complex structure on a smooth leaf space and equip the generalized contact manifold with a principal bundle structure whose connection is defined by the generalized contact data. Under mild assumptions, we show that the curvature induces a symplectic foliation on the leaf space. Several examples are provided.