3-Manifolds with Constant Ricci Eigenvalues $(\lambda ,\lambda ,0)$

Abstract

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.

26 pages, 5 figures