Light cone and Weyl compatibility of conformal and projective structures
Abstract
In the literature different concepts of compatibility between a projective structure and a conformal structure on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than compatibility in the Riemannian sense. An often cited paper [Ehlers-Pirani-Schild:1972] introduces still another criterion which is natural from the physical point of view: every light like geodesics of of the conformal structure is a geodesics of the projective structure. Their claim that this type of compatibility is sufficient for introducing a Weylian metric has recently been questioned in [Trautman:2012] and [Scholz:2019]. Here it is proved that the conjecture of EPS is correct.
Cite
@article{arxiv.2001.01494,
title = {Light cone and Weyl compatibility of conformal and projective structures},
author = {Vladimir S. Matveev and Erhard Scholz},
journal= {arXiv preprint arXiv:2001.01494},
year = {2020}
}
Comments
easy reading/comments are welcome