Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces

Brenden Balch, Chris Peterson, Clayton Shonkwiler

备注：: 17 pages, 4 figures
发表信息：: Differential Geometry and its Applications 74 (2021), 101712
DOI：: 10.1016/j.difgeo.2020.101712

英文摘要：

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.

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