The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds

Abstract

Given any rectangular polyhedron 3-manifold $P$ 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 $P$.

arXiv commentThe argument in this paper is based on an earlier result where we have discovered a major flaw in the argument