The Three Gap Theorem and Riemannian Geometry
Differential Geometry
2008-03-11 v1
Abstract
The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions modulo 1 of the first n multiples of p. Regarding it as a statement about rotations of the circle, we find results in a similar spirit pertaining to isometries of compact Riemannian manifolds and the distribution of points along their geodesics.
Cite
@article{arxiv.0803.1250,
title = {The Three Gap Theorem and Riemannian Geometry},
author = {Ian Biringer and Benjamin Schmidt},
journal= {arXiv preprint arXiv:0803.1250},
year = {2008}
}
Comments
18 pages