On compact manifolds admitting indefinite metrics with parallel Weyl tensor

Abstract

Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such manifolds, namely, vanishing of the Euler characteristic and real Pontryagin classes, and infiniteness of the fundamental group. We also show that, in the Lorentzian case, each of them is at least 5-dimensional and admits a two-fold cover which is a bundle over the circle.

20 pages

References in corpus (1)

• The local structure of conformally symmetric manifolds

Cited by in corpus (6)

• Completeness of compact Lorentzian manifolds with Abelian holonomy
• Curvature Properties of Gödel metric
• Compact pseudo-Riemannian manifolds with parallel Weyl tensor
• The topology of compact rank-one ECS manifolds
• Global properties of indefinite metrics with parallel Weyl tensor
• The metric structure of compact rank-one ECS manifolds