Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds
Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds
We determine the local structure of all pseudo-Riemannian manifolds of dimensions greater than 3 whose Weyl conformal tensor is parallel and has rank 1 when treated as an operator acting on exterior 2-forms at each point. If one fixes three discrete parameters: the dimension, the metric signature (with at least …