Lightlike Cartan geometries are introduced as Cartan geometries modelled on the future lightlike cone in Lorentz-Minkowski spacetime. Then, we provide an approach to the study of lightlike manifolds from this point of view. It is stated that every lightlike Cartan geometry on a manifold N provides a lightlike metric h with radical distribution globally spanned by a vector field Z. For lightlike hypersurfaces of a Lorentz manifold, we give the condition that characterizes when the pull-back of the Levi-Civita connection form of the ambient manifold is a lightlike Cartan connection on such hypersurface. In the particular case that a lightlike hypersurface is properly totally umbilical, this construction essentially returns the original lightlike metric. From the intrinsic point of view, starting from a given lightlike manifold (N, h), we show a method to construct a family of ambient Lorentzian manifolds that realize (N, h) as a hypersurface. This method is inspired on the Feffermann-Graham ambient metric construction in conformal geometry and provides a lightlike Cartan geometry on the original manifold when (N, h) is generic.

引入了类似Cartan的几何形状，作为在Lorentz-Minkowski时空中对未来的锥形圆锥建模的Cartan几何形状。然后，从这一观点出发，我们提供了一种研究轻型流形的方法。据指出，流形N上的每一个类似灯的Cartan几何图形都提供了一个像灯的度量h，其基数分布总体上由矢量场Z跨越。对于Lorentz流形的轻型超曲面，我们给出了这样的条件，该条件表征了环境流形的Levi-Civita连接形式的回拉是此类超曲面上的轻型Cartan连接。在特定的情况下，一个类似灯的超曲面完全是完全脐带的，这种结构实质上会返回原始的类似灯的度量。从内在的角度来看，从给定的光形流形（N，  h）开始，我们展示了一种构造实现（N，  h的环境洛伦兹流形家族的方法）作为超曲面。此方法的启发是采用保形几何学的Feffermann-Graham环境度量结构，并且当（N，  h）为通用时，可以在原始流形上提供类似光的Cartan几何学。