Markus conjecture for closed flat affine manifolds

Let $M$ be a connected closed flat affine manifold. Its holonomy morphism is a map $\rho\colon\pi_1(M,p)\to\mathbf{R}^n\rtimes\operatorname{GL}(n,\mathbf{R})$, and $M$ has parallel volume when $\rho$ takes values in $\mathbf{R}^n\rtimes\operatorname{SL}(n,\mathbf{R})$. The manifold is complete when its developing map $D\colon\widetilde M\to\mathbf{R}^n$ is a diffeomorphism.

Markus conjecture. Any connected closed flat affine manifold with parallel volume is complete.

This conjecture concerns the relationship between the volume-preserving holonomy condition and completeness of flat affine structures. It is still an open question, even in dimension three.