Advanced Search

We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_{1}M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the unit tangent sphere bundle of a Riemannian surface.