Abstract
This paper deals with weakly Ricci-symmetric lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field. We prove that, in a weakly Ricci symmetric lightlike -Einstein (or Einstein) hypersurface of an indefinite Sasakian manifold, the associated 1-forms and satisfy (Theorem 4). Also, we show that there exist no weakly Ricci symmetric screen locally (or globally) conformal lightlike hypersurfaces of indefinite Sasakian manifolds with cyclic parallel Ricci tensor if is not everywhere zero (Theorem 5). A particular case of weakly Ricci symmetric condition is studied and we prove that a special weakly Ricci symmetric screen locally (or globally) conformal lightlike hypersurface cannot be -Einstein (or Einstein) and under certain condition, it cannot be -mixed-totally geodesic (Theorem 7).
Aknowledgments
Main results were done when the author was visiting The Abdus Salam International Centre for Theoretical Physics (ICTP) in the summer of 2007. He thanks that centre for the support during this work. He is also grateful to the referee for helping him to improve the presentation.
Citation
Fortuné Massamba. "On weakly Ricci symmetric lightlike hypersurfaces of indefinite Sasakian manifolds." SUT J. Math. 44 (2) 181 - 201, June 2008. https://doi.org/10.55937/sut/1234383504
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