An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds

Abstract

Purpose – The purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not. Design/methodology/approach – The paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not. Findings – The geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds. Originality/value – All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

Keywords

• Metallic semi-Riemannian manifolds
• Warped product lightlike submanifolds
• Irrotational lightlike submanifolds