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Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces

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arxiv 2004.13196 v1 pith:3JKWHDSN submitted 2020-04-27 math.DG math.GTmath.MG

Brenden Balch , Chris Peterson , Clayton Shonkwiler This is my paper · ORCID
classification math.DGmath.GTmath.MG
keywords lensspacesformulaballsfunctionhomogeneousmomentmoments
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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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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 23 citations worldwide. Full citation record

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    cs.LO 2026-07 accept novelty 8.5 of 10

    BVAS reachability is decidable because non-reachability is always witnessed by a semilinear inductive invariant, yielding a simple enumerative algorithm.

  2. Supermaps on generalised theories

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  3. On the Reachability Problem for Two-Dimensional Branching VASS

    cs.LO 2025-06 accept novelty 8.0 of 10

    The reachability set of every 2-dimensional branching VASS has a computable semilinear representation, so reachability is decidable for this class.

  4. An Intuitionistic Glance at Primes

    math.LO 2025-11 reject novelty 3.0 of 10

    Claims a realizability barrier prevents Heyting Arithmetic from uniformly extracting prime witnesses, making Goldbach-type theorems constructively unrealizable; the barrier fails because primality is decidable by boun...

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