  We consider complete Riemannian $3$-manifolds whose Ricci tensors have
constant eigenvalues $(\lambda, \lambda, 0)$. When $\pi_1$ is finitely
generated, we classify the topology of such manifolds by showing that they have
a free fundamental group if non-trivial and that every free group is obtained.
We give a description up to isometry, when the metric is locally irreducible or
when it is analytic.
