论文标题
均匀镜头空间中距离和球体积的分布
Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces
论文作者
论文摘要
镜头空间是一系列流形的家族，它是拓扑和差异几何形状中许多有趣现象的来源。它们的具体结构，作为有限循环基团的自由线性作用作为奇数球的商，可以更深入地分析其结构。在本文中，我们考虑了均匀三维透镜空间上随机选择的点对点之间的距离功能的矩问题。我们给出了矩矩的递归关系，$ k $ th时刻的公式以及当时生成函数的公式，以及这些镜头空间中所有半径的球体积的明确公式。
Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-dimensional spheres by a free linear action of a finite cyclic group, allows a deeper analysis of their structure. In this paper, we consider the problem of moments for the distance function between randomly selected pairs of points on homogeneous three-dimensional lens spaces. We give a derivation of a recursion relation for the moments, a formula for the $k$th moment, and a formula for the moment generating function, as well as an explicit formula for the volume of balls of all radii in these lens spaces.
