论文标题
关于Riemannian几何图形的Finsler和Lorentz几何形状之间联系的帐户
An account on links between Finsler and Lorentz Geometries for Riemannian Geometers
论文作者
论文摘要
在过去的几年中，洛伦兹和芬斯勒几何形状之间的一些联系已经开发出来，甚至对Riemannian案件进行了申请。我们的目的是简要描述它们，这可以作为最近参考文献的介绍。作为一个激励人物的例子，我们从Zermelo导航问题开始，其中已知的Finslerian描述允许Lorentzian图片对原始问题有完整的几何理解。 Then, we develop some issues including: (a) the accurate description of the Lorentzian causality using Finsler elements, (b) the non-singular description of some Finsler elements (such as Kropina metrics or complete extensions of Randers ones with constant flag curvature), (c) the natural relation between the Lorentzian causal boundary and the Gromov and Busemann ones in the Finsler setting, and (d) practical applications to海浪和火偏向的传播。
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent references. As a motivating example, we start with Zermelo navigation problem, where its known Finslerian description permits a Lorentzian picture which allows for a full geometric understanding of the original problem. Then, we develop some issues including: (a) the accurate description of the Lorentzian causality using Finsler elements, (b) the non-singular description of some Finsler elements (such as Kropina metrics or complete extensions of Randers ones with constant flag curvature), (c) the natural relation between the Lorentzian causal boundary and the Gromov and Busemann ones in the Finsler setting, and (d) practical applications to the propagation of waves and firefronts.
