Geometrical aspects of paracontact pair structures (Q461955)

In the present paper the notion of (metric) paracontact pair structure is introduced, and some geometrical properties of it characteristic foliations are investigated. Also, the normal paracontact pair structures are considered and necessary and sufficient conditions for a paracontact pair structure to be normal are obtained. In particular a version of Morimoto theorem for product manifolds is obtained, and a method is described to obtain a metric paracontact pair structure on the total space of a principal \(S^1\)-bundle via the Boothby-Wang construction.