In this note, some basic structural conditions that are imposed on a Finsler manifold as a consequence of existence of a conformal gradient field are presented. Then, after reiterating the definition of warped product Finsler manifolds and the constituents of its related variational problem, the correlation between geodesics of this warped product structure and geodesics of its constructing Finsler manifolds is studied.

中文翻译：

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Finsler 流形上的共形梯度场

在本笔记中，介绍了由于共形梯度场的存在而强加在 Finsler 流形上的一些基本结构条件。然后，在重申翘曲积Finsler流形的定义及其相关变分问题的构成后，研究了翘曲积结构的测地线与其构造Finsler流形的测地线之间的相关性。