We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical, isoparametric and Einstein null hypersurfaces in Lorentzian space forms and provide several classification results.

中文翻译：

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半黎曼流形中的零屏准共形超曲面及其应用

我们引入了一类半黎曼流形的零超曲面，即屏幕准共形超曲面，其几何形状可以通过其屏幕分布的几何形状进行研究。特别是，这个概念允许我们将先前工作的一些结果扩展到环境空间的截面曲率不为零的情况。作为应用，我们研究了洛伦兹空间形式的脐带、等参和爱因斯坦零超曲面，并提供了几种分类结果。