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arXiv · 2001.01494

Light cone and Weyl compatibility of conformal and projective structures

Vladimir S. Matveev·Erhard Scholz
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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.

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Vladimir S. Matveev, Erhard Scholz. 2020-01-06. Light cone and Weyl compatibility of conformal and projective structures. https://doi.org/10.1007/s10714-020-02716-9

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