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RETRACTED - THE KRONECKER–WEYL EQUIDISTRIBUTION THEOREM AND GEODESICS IN 3-MANIFOLDS

Published online by Cambridge University Press:  21 March 2022

J. BECK
Affiliation:
Department of Mathematics, Hill Center for the Mathematical Sciences, Rutgers University, Piscataway, NJ08854, USA e-mail: [email protected]
W. W. L. CHEN*
Affiliation:
Department of Mathematics and Statistics, Macquarie University, Sydney, NSW2109, Australia

Abstract

Given any rectangular polyhedron $3$ -manifold $\mathcal {P}$ tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in $\mathcal {P}$ .

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Dzmitry Badziahin

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