Finsler manifolds with a special class of \(g\)-natural metrics (Q897406)

The authors study the horizontal and vertical distributions of a class of \(g\)-natural metrics on the tangent bundles of Finsler manifolds. They characterize the Riemannian manifolds among Finsler manifolds from the viewpoint of the geometry of the slit tangent bundle and obtain some results on the Riemannian curvature of these metrics. Finally, they prove that if the slit tangent bundle is locally symmetric, then the base manifold is locally Euclidean.