Abstract
We show that a compact affine manifold endowed with an affine Anosov transformation is finitely covered by a complete affine nilmanifold. This is a partial answer of a conjecture of Franks for affine manifolds.
Highlights
An n-affine manifold M, ∇M is an n-differentiable manifold M endowed with a locally flat connection ∇M, that is a connection ∇M whose curvature and torsion forms vanish identically
We show that a compact affine manifold endowed with an affine Anosov transformation is finitely covered by a complete affine nilmanifold
This is a partial answer of a conjecture of Franks for affine manifolds
Summary
We show that a compact affine manifold endowed with an affine Anosov transformation is finitely covered by a complete affine nilmanifold. This is a partial answer of a conjecture of Franks for affine manifolds.
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