An $n$-dimensional affine manifold $M$ is a topological manifold which admits a system of charts such that the coordinate changes are affine transformations i.e. in $GL(n,\mathbb{R}^n)\rtimes \mathbb{R}^n$. $\mathbb{R}^n$ and Tori $\mathbb{R}^n/\mathbb{Z}^n$ are examples of affine manifolds but what are other examples?
In a similar way, we can defined an integral affine manifold by imposing coordinate change to be in $GL(n,\mathbb{Z}^n)\rtimes \mathbb{Z}^n$. What example of these are known?
Since they have constant metric, I guess there won't be many.
