Screen Cauchy–Riemann (SCR)-lightlike submanifolds of metallic semi-Riemannian manifolds

Purpose The screen Cauchy–Riemann (SCR)-lightlike submanifold is an important class of submanifolds of semi-Riemannian manifolds. It contains various other classes of submanifolds as its sub-cases. It has been studied under various ambient space. The purpose of this research is to study the geometry of SCR-lightlike submanifolds of metallic semi-Riemannian manifolds. Design/methodology/approach The article is divided into five sections. The first section is introductory section which represents brief overview of the conducted research of this article. The second section outlines the key results that are utilized throughout the paper. In section three, the definition of SCR-lightlike submanifold is constructed with one non-trivial example. In section four and five, the important results on integrability, totally geodesic foliations and warped product are given. Findings The SCR-lightlike submanifold is introduced. One non-trivial example is constructed which helps to understand the given structure. The necessary and sufficient conditions for the integrability and to be totally geodesic for various distributions are obtained. The necessary and sufficient conditions for induced connection on totally umbilical SCR-lightlike submanifolds to be a metric connection are discussed. Various results are found on totally umbilical SCR-lightlike submanifolds. Finally, the existence of the warped product lightlike submanifold of the type N ⊥ × λ N T is studied. Originality/value SCR-lightlike submanifolds have been explored within ambient manifolds possessing various structures, such as Kaehler, Sasakian and Kenmotsu structures. In this article, we investigate this structure on submanifolds of metallic semi-Riemannian manifolds. This original and authentic research will aid researchers in advancing the study of semi-Riemannian manifolds.