Finsler generalization of the Tamm metric

We study manifolds of the Finsler type whose tangent $($pseudo-$)$Riemannian spaces are invariant under the $($pseudo$)$orthogonal group. We construct the Cartan connection and study geodesics, extremals, and also motions. We establish that if the metric tensor of the space is a homogeneous tensor of the zeroth order with respect to the coordinates of the tangent vector, then the metric of the tangent space is realized on a cone of revolution. We describe the structure of geodesics on the cone as trajectories of motion of a free particle in a central field.