New examples of compact Weyl-parallel manifolds

Abstract

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.

arXiv commentadded several references and expanded the Introduction

References in corpus (7)

• Completeness of compact Lorentzian manifolds with Abelian holonomy
• Two-symmetric Lorentzian manifolds
• Compact pseudo-Riemannian manifolds with parallel Weyl tensor
• On Closed Manifolds with Harmonic Weyl Curvature
• The topology of compact rank-one ECS manifolds
• On conformally recurrent manifolds of dimension greater than 4
• Compact locally homogeneous manifolds with parallel Weyl tensor

Cited by in corpus (3)

• The metric structure of compact rank-one ECS manifolds
• Compact locally homogeneous manifolds with parallel Weyl tensor
• Rank-one ECS manifolds of dilational type