TITLE:
Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds
AUTHORS:
Domitien Ndayirukiye, Gilbert Nibaruta, Ménédore Karimumuryango, Aboubacar Nibirantiza
KEYWORDS:
Lightlike (Sub)Manifolds, Algebraic Curvature Tensor, Total Umbilicity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.12,
December
19,
2019
ABSTRACT: 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.