NOTES ON THE GEOMETRY OF COTANGENT BUNDLE AND UNIT COTANGENT SPHERE BUNDLE

Let (N, g) be a Riemannian manifold, by using the musical isomorphisms (sic) and (sic) induced by g, we built a bridge between the geometry of the tangent bundle TN (resp. the unit tangent sphere bundle T1N) equipped with the Sasaki metric g(S) (resp. the induced Sasaki metric (g) over bar (S)) and that of the cotangent bundle T*N (resp. the unit cotangent sphere bundle T*N-1) endowed with the Sasaki metric g((S) over tilde) (resp. the induced Sasaki metric (g) over tilde ((S) over tilde)). Moreover, we prove that T*N-1 carries a contact metric structure and study some of its properties.