×

Killing and geodesic lightlike hypersurfaces of indefinite Sasakian manifolds. (English) Zbl 1157.53013

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.

MSC:

53B25 Local submanifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Citations:

Zbl 0848.53001
PDFBibTeX XMLCite