In this paper, we study affine manifolds endowed with linear foliations. These are foliations defined by vector subspaces invariant by the linear holonomy. We show that an n-dimensional compact, complete, and oriented affine manifold endowed with a codimension 1 linear foliation F is homeomorphic to the n-dimensional torus if the leaves of F are simply connected. Let (M, del(M)) be a 3-dimensional compact affine manifold endowed with a codimension 1 linear foliation. We prove that (M, del(M)) has a finite cover which is homeomorphic to the total space of a bundle over the circle if its developing map is injective, and has a convex image. (C) 2021 Elsevier B.V. All rights reserved.
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