The Three Gap Theorem and Riemannian Geometry

Ian Biringer; Benjamin Schmidt

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arXiv · 0803.1250

The Three Gap Theorem and Riemannian Geometry

Ian Biringer·Benjamin Schmidt

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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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Ian Biringer, Benjamin Schmidt. 2008-03-08. The Three Gap Theorem and Riemannian Geometry. https://arxiv.org/abs/0803.1250

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