Local structure of generalized contact manifolds

Generalized contact pairs were introduced in Poon and Wade (2011) [25]. In this paper, we carry out a detailed study of geometric properties of these structures. First, we give geometric conditions expressing the integrability of a generalized contact pair. Then, we use them to obtain insights into the characteristic foliation of a generalized contact manifold. Finally we show that, locally, any smooth manifold endowed with a generalized contact pair is equivalent to the product of an almost cosymplectic manifold whose associated 2-form is closed by a generalized complex manifold.