# Remarks on screen integrable null hypersurfaces in Lorentzian manifolds

## TL;DR

This paper investigates the geometry of screen integrable null hypersurfaces in Lorentzian manifolds, showing they can be generated from isometric immersions into semi-Euclidean spaces, and characterizing their geometric properties.

## Contribution

It establishes a link between null hypersurfaces and isometric immersions into semi-Euclidean spaces, providing conditions under which these hypersurfaces are umbilic and screen totally umbilic.

## Key findings

- Null hypersurfaces are necessarily umbilic and screen totally umbilic.
- Such hypersurfaces can be generated from isometric immersions of their screen distribution leaves.
- Immersions are contained in semi-Euclidean spheres or hyperbolic spaces under certain conditions.

## Abstract

In the present paper, we show that the geometry of a screen integrable null hypersurface can be generated from an isometric immersion of a leaf of its screen distribution into the ambient space. We prove, under certain geometric conditions, that such immersions are contained in semi-Euclidean spheres or hyperbolic spaces, and the underlying null hypersurfaces are necessarily umbilic and screen totally umbilic. Where necessary, examples have been given to illustrate the main ideas.