The Three Gap Theorem and Riemannian Geometry

2008/03/08 by Ian Biringer, Biringer, Ian, Benjamin Schmidt +1 · 1 citation
Mathematics · #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C22

paper · pdf · doi:10.48550/arxiv.0803.1250

18 pages

arxiv created 2008/03/08 · arxiv updated 2009/12/01

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.

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