Characterization of the Unit Tangent Sphere Bundle with $ g $-Natural Metric and Almost Contact B-metric Structure

Abstract

We consider unit tangent sphere bundle of a Riemannian manifold $ (M,g) $ as a $ (2n+1) $-dimensional manifold and we equip it with pseudo-Riemannian $ g $-natural almost contact B-metric structure. Then, by computing coefficients of the structure tensor $ F$, we completely characterize the unit tangent sphere bundle equipped to this structure, with respect to the relevant classification of almost contact B-metric structures, and determine a class such that the unit tangent sphere bundle with mentioned structure belongs to it. Also, we find some curvature conditions such that the mentioned structure satisfies each of eleven basic classes.