$H$-contact unit tangent sphere bundles of Riemannian manifolds

TL;DR

This paper characterizes when the unit tangent bundle of a Riemannian manifold has an $H$-contact structure, showing it occurs precisely when the base manifold is 2-stein, linking contact geometry with curvature conditions.

Contribution

It establishes a necessary and sufficient condition for the unit tangent bundle to be $H$-contact, connecting contact metric structures with the 2-stein property of the base manifold.

Findings

Unit tangent bundle is $H$-contact iff the base manifold is 2-stein.

Provides a characterization linking contact geometry and curvature conditions.

Enhances understanding of geometric structures on tangent bundles.

Abstract

A contact metric manifold is said to be $H$-contact, if the characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold $M$ equipped with the standard contact metric structure is $H$-contact if and only if $M$ is $2$-stein.