On the Characteristic Foliations of Metric Contact Pairs

TL;DR

This paper studies metric contact pairs on manifolds, showing that associated metrics have identical volume elements and that characteristic foliation leaves are minimal, with examples illustrating their geometric properties.

Contribution

It demonstrates that all metrics associated with a contact pair share the same volume element and that the characteristic foliation leaves are minimal, expanding understanding of their geometric structure.

Findings

All associated metrics have the same volume element.

Leaves of characteristic foliations are minimal.

An example where leaves are not totally geodesic.

Abstract

A contact pair on a manifold always admits an associated metric for which the two characteristic contact foliations are orthogonal. We show that all these metrics have the same volume element. We also prove that the leaves of the characteristic foliations are minimal with respect to these metrics. We give an example where these leaves are not totally geodesic submanifolds.