W. Roter

Walker's theorem without coordinates

We provide a coordinate-free version of the local classification, due to Walker [Q. J. Math. 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as the total space of a fiber bundle, each fiber of which is an affine principal bundle over a pseudo-Riemannian manifold. All structures just named are naturally determined by the distribution and the metric, in contrast with the noncanonical choice of coordinates in the usual formulation of Walker’s theorem.

Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds

We determine the local structure of all pseudo-Riemannian manifolds

On compact manifolds admitting indefinite metrics with parallel Weyl tensor

(M,g)

On conformally symmetric Ricci-recurrent spaces

in dimensions

On conformally recurrent Ricci-recurrent manifolds

n\ge4

On conformally symmetric manifolds with metrics of indices 0 and 1

whose Weyl conformal tensor

The local structure of conformally symmetric manifolds

W

Some theorems on conformally symmetric manifolds

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

Compact pseudo-Riemannian manifolds with parallel Weyl tensor

n\ge4

On the existence of certain conformally recurrent metrics

, the metric signature