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arXiv · 2004.13196

Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces

Brenden Balch·Chris Peterson·Clayton Shonkwiler
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Abstract

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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Brenden Balch, Chris Peterson, Clayton Shonkwiler. 2020-04-27. Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces. https://doi.org/10.1016/j.difgeo.2020.101712

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