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.

easy reading/comments are welcome

References in corpus (5)

• Geometric realizations, curvature decompositions, and Weyl manifolds
• A criterion for compatibility of conformal and projective structures
• On Kähler metrisability of two-dimensional complex projective structures
• Weyl metrisability of two-dimensional projective structures
• A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection

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• Geometry from geodesics: fine-tuning Ehlers, Pirani, and Schild
• Statistical Geometry and Hessian Structures on Pre-Leibniz Algebroids