Geometrical Aspects of Paracontact Pair Structures

Abstract

We introduce the notion of (metric) paracontact pair structure and establish certain properties of the characteristic foliations associated to it. We also consider normal paracontact pair structures and provide necessary and sufficient conditions for a paracontact pair structure to be normal. In particular, we formulate an analogue of Morimoto's theorem for product manifolds. Finally, we describe a way to obtain a metric paracontact pair structure on the total space of a principal $\mathbb{S}^1$-bundle via the Boothby-Wang construction.