Massamba, Fortuné Killing and geodesic lightlike hypersurfaces of indefinite Sasakian manifolds. (English) Zbl 1157.53013 Turk. J. Math. 32, No. 3, 325-347 (2008). The notion of light-like submanifold of a semi-Riemannian manifold was introduced by [A. Bejancu and K. L. Duggal, Light-like Submanifolds of Semi-Riemannian Manifolds and Applications. Mathematics and its Applications. 364. (Dordrecht): Kluwer Academic Publishers (1996; Zbl 0848.53001)]. Several authors have studied a light-like hypersurface of a semi-Riemannian manifold. In this paper, the author studies some properties of a light-like hypersurface of an indefinite Sasakian manifold. Under certain conditions the existence of Killing and geodesic light-like hypersurfaces is proved in this framework as well as that of parallel vector fields. Several characterizations of \(D\)-totally geodesic and mixed totally geodesic light-like hypersurfaces are presented with interesting examples. Reviewer: Constantin Călin (Iaşi) Cited in 2 Documents MSC: 53B25 Local submanifolds 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics Keywords:light-like submanifold; indefinite Sasakian manifold Citations:Zbl 0848.53001 PDFBibTeX XMLCite \textit{F. Massamba}, Turk. J. Math. 32, No. 3, 325--347 (2008; Zbl 1157.53013)