New examples of compact Weyl-parallel manifolds

We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metric signatures in all dimensions $n\ge 5$. Until now such manifolds were only known to exist in dimensions $n=3j+2$, where $j$ is any positive integer [11]. As in [11], our examples are diffeomorphic to nontrivial torus bundles over the circle and arise from a quotient-manifold construction applied to suitably chosen discrete isometry groups of diffeomorphically-Euclidean “model” manifolds.