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arXiv math/0608515math.DG
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流形上两个互不相关的Finsler结构

Two nonrelated Finsler structures on a manifold

Aly A. Tamim, Nabil L. Youssef

备注：
8 pages, LaTeX file
发表信息：
Rev. Roumaine Math. Pures Appl., Vol. 45, 4(2000), 713-722
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摘要：

本文考虑同一基流形$M$上的两个不同的{ \em Finsler}结构$L$和$L^*$，它们之间没有任何关系. \par引入$π$ -张量场表示与$L$和$L^*$相关联的Cartan连接之间的差异，我们研究了与$L$和$L^*$相关联的几何对象具有相同属性的条件。在本文的研究项目中，我们考虑的性质是测地线，雅可比场，Berwald流形，局部Minkowski流形和Landsberg流形。\par应当注意，我们的方法是内在的，即，它不使用局部坐标技术。

英文摘要：

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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