Null screen isoparametric hypersurfaces in Lorentzian space forms

TL;DR

This paper introduces the concept of screen isoparametric hypersurfaces in null hypersurfaces within Lorentzian space forms, deriving Cartan identities and providing local characterizations.

Contribution

It develops a new formalism for null hypersurfaces in Lorentzian geometry and derives fundamental identities and characterizations for these hypersurfaces.

Findings

Derived Cartan identities for screen principal curvatures.

Provided local characterization of null screen hypersurfaces.

Extended the theory of isoparametric hypersurfaces to null hypersurfaces in Lorentzian spaces.

Abstract

In this paper we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson-Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersurfaces.