On tangent sphere bundles with contact pseudo-metric structures

TL;DR

This paper studies contact pseudo-metric structures on tangent sphere bundles, establishing conditions under which these structures are $(,)$-contact or K-contact, linked to the base manifold's constant curvature.

Contribution

It introduces a contact pseudo-metric structure on tangent sphere bundles and characterizes when these are $(,)$-contact or K-contact based on the base manifold's curvature.

Findings

Tangent sphere bundle is $(,)$-contact pseudo-metric iff the base manifold has constant sectional curvature.

The structure is K-contact iff the base manifold has constant curvature $$.

Provides a characterization linking contact structures on tangent sphere bundles to curvature properties.

Abstract

In this paper, we introduce a contact pseudo-metric structure on a tangent sphere bundle $T_\varepsilon M$. we prove that the tangent sphere bundle $T_{\varepsilon}M$ is $(\kappa, \mu)$-contact pseudo-metric manifold if and only if the manifold $M$ is of constant sectional curvature. Also, we prove that this structure on the tangent sphere bundle is $K$-contact iff the base manifold has constant curvature $\varepsilon$.