论文标题
在Hamel-Funk功能模型上喷雾剂
Sprays on Hamel-Funk Functions Model
论文作者
论文摘要
喷雾的Hamel功能在研究相关喷雾剂的投影式衡量性的研究中起着重要作用，而Funk功能是特殊的Hamel功能。 Finsler公制是公制本身引起的喷雾剂的特殊Hamel功能，而放克度量是Minkowski喷雾的特殊放克功能。在本文中，我们在Hamel或Funk功能模型上研究喷雾。首先，我们提供了喷雾剂的Hamel或Funk功能的一些基本特性，以及在投影关系中的Hamel或Funk功能的一些曲率特性。我们使用Funk Metric来建造一个喷雾剂，并获得其一些曲率特性及其衡量条件。其次，我们考虑在某些喷雾歧管上存在放克功能的存在。我们证明，在R-Flat喷雾歧管上存在局部放克功能，并且在某些投影式平坦的Berwald喷雾歧管上，我们构建了多种非零Funk功能。最后，我们介绍了与给定喷雾剂，哈默尔或放克功能相关的名为Hamel或Funk Sprays的新喷雾剂。我们获得了标量曲率的Hamel或Funk喷雾的一些特殊特性，尤其是在其衡量性和特殊形式的Riemann曲率上。
Hamel functions of a spray play an important role in the study of the projective metrizability of the concerned spray, and Funk functions are special Hamel functions. A Finsler metric is a special Hamel function of the spray induced by the metric itself and a Funk metric is a special Funk function of a Minkowski spray. In this paper, we study sprays on a Hamel or Funk function model. Firstly, we give some basic properties of a Hamel or Funk function of a spray and some curvature properties of a Hamel or Funk function in projective relations. We use the Funk metric to construct a family of sprays and obtain some of their curvature properties and their metrizability conditions. Secondly, we consider the existence of Funk functions on certain spray manifold. We prove that there exist local Funk functions on a R-flat spray manifold, and on certain projectively flat Berwald spray manifolds, we construct a multitude of nonzero Funk functions. Finally, we introduce a new class of sprays called Hamel or Funk sprays associated to given sprays and Hamel or Funk functions. We obtain some special properties of a Hamel or Funk spray of scalar curvature, especially on its metrizability and a special form of its Riemann curvature.
