Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications

TL;DR

This paper introduces a new class of null hypersurfaces called screen quasi-conformal hypersurfaces in semi-Riemannian manifolds, extending existing results to spaces with non-zero sectional curvature and classifying special types in Lorentzian space forms.

Contribution

It defines and studies the geometry of screen quasi-conformal null hypersurfaces, extending prior results to non-zero curvature spaces and providing classification theorems for special null hypersurfaces.

Findings

Extended results to semi-Riemannian manifolds with non-zero curvature

Classified umbilical, isoparametric, and Einstein null hypersurfaces in Lorentzian space forms

Developed a framework for analyzing null hypersurfaces via their screen distribution

Abstract

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.