Pseudo-Szabó Operators and Lightlike Szabó Hypersurfaces

Abstract

In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators associated to algebraic covariant derivative curvature maps (tensors) to lightlike hypersurfaces. Some examples are given with explicit determination of their Szabó operators. Finally, we introduce the notion of lightlike Szabó hypersurfaces and give some characterization results of locally symmetric lightlike hypersurfaces and semi-symmetric lightlike hypersurfaces from Szabó condition.