We consider the unit tangent sphere bundle of Riemannian ̃ and we equip it to an almost manifold (M, g) with g-natural metric G contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ̃ More precisely, we prove that (M, g) and local symmetry property of G. the flatness of metric g is necessary and sufficient for the g-natural metric ̃ to be locally symmetric.
