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The Three Gap Theorem and Riemannian geometry

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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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Authors and Affiliations

  1. University of Chicago, Chicago, USA

    Ian Biringer & Benjamin Schmidt

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  1. Ian Biringer
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  2. Benjamin Schmidt
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Correspondence to Ian Biringer.

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Biringer, I., Schmidt, B. The Three Gap Theorem and Riemannian geometry. Geom Dedicata 136, 175–190 (2008). https://doi.org/10.1007/s10711-008-9283-8

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  • DOI: https://doi.org/10.1007/s10711-008-9283-8

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