In the conformal (Möbius) geometry of submanifolds, using algebraic invariants of the shape operator to construct conformal invariants is a frequently used method. But it does not apply to [Formula: see text]-dim Lorentzian hypersurfaces of the last type, the minimal polynomial of whose shape operator has a triple root. In this paper, using the obstruction of some distribution to be integrable, a new method to construct conformal invariants is introduced. Using this method, a complete conformal invariant system is constructed for generic conformally flat Lorentzian hypersurfaces of the last type. We find that such kind of hypersurfaces allows an infinite parameter family of non-equivalent deformations, which implies they are more abundant than the other three types. For non-generic conformally flat Lorentzian hypersurfaces of the last type, the isometric geometry is studied and a fundamental theorem is obtained in this paper.

中文翻译：

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具有特殊形状算子的洛伦兹 4 空间共形平坦洛伦兹超曲面

在子流形的共形（莫比乌斯）几何中，使用形状算子的代数不变量来构造共形不变量是一种常用的方法。但它不适用于 [Formula: see text]-dim Lorentzian 超曲面的最后一种类型，其形状算子的最小多项式具有三重根。本文利用某些分布的阻塞可积性，介绍了一种构造共形不变量的新方法。使用这种方法，为最后一种类型的通用共形平坦洛伦兹超曲面构造了一个完整的共形不变系统。我们发现这种超曲面允许无限参数族的非等效变形，这意味着它们比其他三种类型更丰富。对于最后一种类型的非泛型共形平坦洛伦兹超曲面，