Two nonrelated Finsler structures on a manifold

Details Two nonrelated Finsler structures on a manifold Two nonrelated Finsler structures on a manifold

2006-08-21

arxiv.org/abs/math/0608515v1

Rev. Roumaine Math. Pures Appl., Vol. 45, 4(2000), 713-722

Mathematics

Differential Geometry

8 pages, LaTeX file

Scientific paper

In the present paper, we consider two different {\em Finsler} structures $L$ and $L^*$ on the same base manifold $M$, with no relation preassumed between them. \par Introducing the $\pi$-tensor field representing the difference between the Cartan connections associated with $L$ and $L^*$, we investigate the conditions, to be satisfied by this $\pi$-tensor field, for the geometric objects associated with $L$ and $L^*$ to have the same properties. Among the items investigated in the paper, we consider the properties of being a geodesic, a Jacobi field, a Berwald manifold, a locally Minkowskian manifold and a Landsberg manifold. \par It should be noticed that our approach is intrinsic, i.e., it does not make use of local coordinate techniques.

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