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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.

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.

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^⊥×_λN_T is studied.

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.

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.

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.

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.

All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.