On compact manifolds admitting indefinite metrics with parallel Weyl tensor
Differential Geometry
2011-06-07 v1
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.
Cite
@article{arxiv.0705.1106,
title = {On compact manifolds admitting indefinite metrics with parallel Weyl tensor},
author = {Andrzej Derdzinski and Witold Roter},
journal= {arXiv preprint arXiv:0705.1106},
year = {2011}
}