Contact pair structures and associated metrics

TL;DR

This paper introduces contact pair structures and associated metrics, demonstrating geometric properties such as geodesic Reeb curves and orthogonal characteristic foliations with induced contact metric structures.

Contribution

It defines contact pair structures with associated metrics and explores their geometric properties, including geodesic Reeb curves and orthogonal characteristic foliations.

Findings

Reeb vector field integral curves are geodesics

Reeb action leaves are totally geodesic

Characteristic foliations are orthogonal with induced contact metric structures

Abstract

We introduce the notion of contact pair structure and the corresponding associated metrics, in the same spirit of the geometry of almost contact structures. We prove that, with respect to these metrics, the integral curves of the Reeb vector fields are geodesics and that the leaves of the Reeb action are totally geodesic. Mreover, we show that, in the case of a metric contact pair with decomposable endomorphism, the characteristic foliations are orthogonal and their leaves carry induced contact metric structures.