Geodesic
Finsler generalization of the~Tamm metric
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 186-197

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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.
Mots-clés : Finsler Tamm space, Cartan connection, motion
Keywords: geodesic. 
@article{TMF_2016_189_2_a2,
     author = {V. I. Panzhenskij and O. P. Surina},
     title = {Finsler generalization of {the~Tamm} metric},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {186--197},
     publisher = {mathdoc},
     volume = {189},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a2/}
}
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V. I. Panzhenskij; O. P. Surina. Finsler generalization of the~Tamm metric. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 186-197. http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a2/