Geodesic
Null hypersurface normalized by the curvature vector field in a Lorentzian manifold of quasi-constant curvature
Theophile Kemajou Mbiakop1 ; Theophile Kemajou Mbiakop
1Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Maroua, Maroua, Cameroon
Acta mathematica Universitatis Comenianae, Tome 94 (2025) no. 2, pp. 87-104 
Theophile Kemajou Mbiakop; Theophile Kemajou Mbiakop. Null hypersurface  normalized by the curvature  vector field in a Lorentzian manifold of quasi-constant curvature. Acta mathematica Universitatis Comenianae, Tome 94 (2025) no. 2, pp. 87-104. http://geodesic.mathdoc.fr/item/AMUC_2025_94_2_a3/
@article{AMUC_2025_94_2_a3,
     author = {Theophile Kemajou Mbiakop and Theophile Kemajou Mbiakop},
     title = { Null hypersurface  normalized by the curvature  vector field in a {Lorentzian} manifold of quasi-constant curvature},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {87--104},
     year = {2025},
     volume = {94},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2025_94_2_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

We introduce a class of null hypersurfaces $M$ of Lorentzian manifolds of quasi-constant curvature $\overline{M}$, namely, $\zeta$-rigging null hypersurfaces, whose curvature vector field $\zeta$ is a rigging for $M$. We extend some well-known results for Lorentzian manifolds of constant curvature and prove several classification theorems for such a null hypersurface. Next, we establish sufficient conditions to guarantee that such a null hypersurface must be totally geodesic. As a consequence, we prove that the ambient manifold is flat along $M$.