Distributions of distances and volumes of balls in homogeneous lens spaces

• Published in: Differential geometry and its applications Vol. 74; p. 101712
• Main Authors: Balch, Brenden, Peterson, Chris, Shonkwiler, Clayton
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-2021
• Subjects: Distance distributions; Homogeneous manifolds; Lens spaces; Moments; secondary; Moments; Homogeneous manifolds; Lens spaces; Distance distributions; primary
• ISSN: 0926-2245; 1872-6984
• DOI: 10.1016/j.difgeo.2020.101712

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 kth 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.