Dirac operators on lightlike hypersurfaces

TL;DR

This paper investigates Dirac operators on lightlike hypersurfaces within 4-dimensional Lorentzian manifolds, deriving formulas that relate these operators to the curvatures of the hypersurface and ambient space.

Contribution

It introduces a spinorial Gauss formula for lightlike hypersurfaces and explores the effects of degenerate metrics on Dirac operators in this context.

Findings

Derived a spinorial Gauss formula for lightlike hypersurfaces

Analyzed the impact of degenerate metrics on Dirac operators

Established relations between Dirac operators and Riemannian curvatures

Abstract

In this study, we obtain a spinorial Gauss formula for a lightlike hypersurface in Lorentzian manifold with 4-dimension. Then, we take into account the changes caused by degenerate metric on hypersurface and investigate Dirac operator for lightlike hypersurface. Later, we establish the relation between Dirac operators and Riemannian curvatures of manifold and hypersurface.