Two nonrelated Finsler structures on a manifold

Aly A. Tamim; Nabil L. Youssef

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arXiv · math/0608515

Two nonrelated Finsler structures on a manifold

Aly A. Tamim·Nabil L. Youssef

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Abstract

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 $π$-tensor field representing the difference between the Cartan connections associated with $L$ and $L^*$, we investigate the conditions, to be satisfied by this $π$-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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BibTeX RIS

Aly A. Tamim, Nabil L. Youssef. 2006-08-21. Two nonrelated Finsler structures on a manifold. https://arxiv.org/abs/math/0608515

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