Author(s)

Domitien Ndayirukiye^1*, Gilbert Nibaruta¹, Ménédore Karimumuryango², Aboubacar Nibirantiza³

¹Ecole Normale Supérieure, Département des Sciences Naturelles, Bujumbura, Burundi.
²Université du Burundi, Institut des Statistiques, Bujumbura, Burundi.
³Université du Burundi, Institut de Pédagogie Appliquée, Département des Mathématiques, Bujumbura, Burundi.

Lightlike warped product manifolds are considered in this paper. The geometry of lightlike submanifolds is difficult to study since the normal vector bundle intersects with the tangent bundle. Due to the degenerate metric, the induced connection is not metric and it follows that the Riemannian curvature tensor is not algebraic. In this situation, some basic techniques of calulus are not useable. In this paper, we consider lightlike warped product as submanifold of semi-Riemannian manifold and establish some remarkable geometric properties from which we establish some conditions on the algebraicity of the induced Riemannian curvature tensor.

Lightlike (Sub)Manifolds, Algebraic Curvature Tensor, Total Umbilicity

Ndayirukiye, D. , Nibaruta, G. , Karimumuryango, M. and Nibirantiza, A. (2019) Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds. Journal of Applied Mathematics and Physics, 7, 3132-3139. doi: 10.4236/jamp.2019.712220.