g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process

Abstract

E. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We prove in this note that every Riemannian g-natural metric on the unit tangent sphere bundle over a Riemannian manifold can be constructed by the Musso-Tricerri’s process. As a corollary, we show that every Riemannian g-natural metric on the unit tangent bundle, over a two-point homogeneous space, is homogeneous.

Keywords

• unit tangent (sphere) bundle
• einstein manifold
• g-natural metric