Finsler generalization of the Tamm metric

Abstract

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.