Half-Lightlike Submanifold of a Lorentzian Manifolds with a conformal co-screen distribution

TL;DR

This paper develops a classification framework for half-lightlike submanifolds in Lorentzian manifolds, extending previous results by deriving Cartan's formula and analyzing conformal co-screen distributions.

Contribution

It introduces Cartan's formula for these submanifolds and classifies them under specific curvature conditions, expanding the understanding of lightlike geometry.

Findings

Half-lightlike submanifolds with conformal co-screen distributions are locally lightlike triple product manifolds.

Classification of such submanifolds with constant screen principal curvatures.

Extension of previous lightlike hypersurface results to broader submanifold classes.

Abstract

In this paper, we give the Cartan's formula for half-lightlike submanifolds of Lorentzian manifolds and use it to show that a screen homothetic half-lightlike submanifolds of a Lorentzian space form, with a conformal co-screen distribution are locally a lightlike triple product manifolds. Then we give a classification theorem for half-lightlike submanifolds of Lorentzian space form with constant screen principal curvatures. These results extend some results obtained in the case of lightlike hypersurfaces of Lorentzian manifolds ([1]).