In a recent past, the growing importance of lightlike submanifolds in global Lorentzian geometry and their extensive use in general relativity, motivated their study in a semi-Riemannian manifold. This is the lightlike geometry of (sub-)manifolds [...]
In this paper, we generalize the Cartan's fundamental formula on lightlike hypersurfaces, then we use it to show that a screen conformal lightlike hypersurface of a Minkowski space is locally a triple product manifold. [...]
ATINDOGBE COMLAN CYRIAQUE [1], HAROUNA MAHAMANE MAHI [2], TOSSA JOEL [3],
Rigging technique introduced in Gutiérrez and Olea (Math Nachr 289:1219–1236, 2016) is a convenient way to address the study of null hypersurfaces. It offers, in addition, the extra benefit of inducing a Riemannian structure on the null hypersurfa [...]
We establish after some technical results a characterization of maximal null hypersurfaces in terms of a constant mean curvature screen foliation (in the slices) induced by the Chen’s vector field. Thereafter, bounds are provided for both the squar [...]
Metric and curvature symmetries (Killing, homothetic, conformal, null con- vergence conditions...) of Riemannian, semi-Riemannian, and lightlike manifolds play an important role in theoretical physics, especially in general relativity. In the prese [...]
We study normalized null hypersurfaces in Brinkmann spacetimes with special attention paid to Plane Fronted Waves. We explore geodesibil- ity criterion and characterization for null hypersurfaces in links with relative position of a global paralle [...]
ATINDOGBE COMLAN CYRIAQUE [1], KEMADJOU THEOPHILE MBIAKOP [1],
We prove that a compact Lorentzian manifold (M, g) admitting a causal Killing vector field is totally vicious or it contains a compact achronal Killing horizon. In particular a compact spacetime which satisfies the null generic condition and admits [...]