Duggal, K. L.; Jin, D. H. Half lightlike submanifolds of codimension 2. (English) Zbl 0995.53051 Math. J. Toyama Univ. 22, 121-161 (1999). The theory of lightlike (degenerate) submanifolds in semi-Riemannian manifolds is relatively new (see, for instance, T. Ikawa [Tsukuba J. Math. 9, 353-371 (1965; Zbl 0588.53017)]). The paper under review deals with the geometry of totally umbilical half-lightlike submanifolds of codimension 2 in a semi-Riemannian manifold. Necessary and sufficient conditions that the Ricci tensor of such a submanifold is symmetric are obtained. Interesting examples of totally umbilical half-lightlike surfaces in \({\mathbb{R}}^4_2\) and \({\mathbb R}^4_1\), respectively, are given. In particular, the authors investigate totally umbilic half-lightlike surfaces in a 4-dimensional space-time manifold. The null Gauss curvature of such a surface vanishes. Sufficient conditions for the vanishing of the null sectional curvature functions are proved. Finally, certain possible research problems are stated. Reviewer: Ion Mihai (Bucureşti) Cited in 1 ReviewCited in 11 Documents MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53B25 Local submanifolds Keywords:semi-Riemannian manifold; half-lightlike submanifolds; totally umbilical submanifold; space-time manifold; Minkowski space Citations:Zbl 0588.53017 PDFBibTeX XMLCite \textit{K. L. Duggal} and \textit{D. H. Jin}, Math. J. Toyama Univ. 22, 121--161 (1999; Zbl 0995.53051)