论文标题
共形结构的光锥和Weyl兼容性
Light cone and Weyl compatibility of conformal and projective structures
论文作者
论文摘要
在文献中，使用了射影结构与可区分歧管上的共形结构之间的兼容性不同的概念。在韦尔几何意义上，尤其是兼容性，而在黎曼的意义上，兼容性比兼容性略微泛滥。经常引用的论文[Ehlers-Pirani-Schild：1972]引入了另一个标准，从物理的角度来看：整形结构的大地测量学之类的每种光都是投射结构的大地测量学。他们声称这种类型的兼容性足以引入Weylian指标，最近在[Trautman：2012]和[Scholz：2019]中受到了质疑。在这里证明，EP的猜想是正确的。
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.
