具有迷向S曲率Randers度量的几何意义

摘要

The Zermelo navigation on Riemannian manifolds provides a succinct and geometric description of Randers metrics. With this description, D. Bao, C. Robles and Z. Shen have completely classified Randers metrics of constant flag curvature. In this paper, I study Randers metrics under the navigation description and discover two sufficient and necessary conditions for Randers metrics of special curvature properties, which are more geometrically meaningful than the traditional description.And several propositions and examples resulted from these conditions are included. Furthermore, I investigate thoroughly with Randers metrics of Berwald type under the navigation description.%Riemann流形上的Zermelo航行为Randers度量提供了一个简洁而且清晰的几何背景.在这个背景下D.Bao,C.Robles和Z.Shen对于具有常旗曲率的Randers度量进行了完全分类.这篇论文中,我得到了判定具有特殊曲率性质的Randers度量的两个充分必要条件.从这两个条件出发,我得到了迷向S曲率的Randers度量的几何意义和一系列推论,并且构造了具有迷向S曲率Randers度量的新例子.最后,在Zermelo航行的背景下研究了Berwald型的Randers度量.