OSSERMAN LIGHTLIKE HYPERSURFACE CASES

Mulebu, Paulin Shakwanda
Mamona, Oscar Lungiambudila
Ta-Yen, Gerard Tawaba Musian
Landa, Alain Musesa
Makiese, Michael Kilela

AL-ULUM: JURNAL SAINS DAN TEKNOLOGI
Vol 11, No 3 (2025)

In this study, we constructed four examples of light-like hypersurfaces that satisfy the conditions of an Osserman manifold, based on the characterisation of light-like hypersurfaces of a pseudo-Riemannian manifold of dimension m+2. To this end, we relied on several theoretical results and propositions, particularly those of DUGAL and BEJANCU, in order to establish the conditions under which a light-like hypersurface  of a pseudo-Riemannian manifold , can be characterized as an Osserman manifold. This characterization is achieved either through the admissible screen distribution  or through the induced algebraic curvature structure. Accordingly, we presented several examples of lightlike hypersurfaces in a semi-Riemannian setting that satisfy the Osserman condition by verifying the required properties of both the Jacobi operator and the induced algebraic curvature.