Abstract
PurposeThe 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/approachThe 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.FindingsThe 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/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.
Highlights
It is well known that the study of semi-Riemannian manifolds and its submanifolds is more complicated as compared to Riemannian manifolds and its submanifolds
Our aim in this paper is to investigate whether it is possible to write lightlike submanifolds of metallic semi-Riemannian manifolds in the form of warped product lightlike submanifolds or not
We introduce the screen real lightlike submanifolds and find that, it is difficult to say that screen real lightlike submanifolds are warped product lightlike submanifolds or not
Summary
It is well known that the study of semi-Riemannian manifolds and its submanifolds is more complicated as compared to Riemannian manifolds and its submanifolds. It is observed that the induced metric on submanifolds of semi-Riemannian manifolds has two cases, either nondegenerate or degenerate. The study of degenerate submanifolds is known as lightlike geometry. Apart from this, the geometry of various submanifolds of metallic and golden semi-Riemannian manifolds have been studied in [10,11,12]. This paper is categorized as follows: In Section 1, we give brief description of lightlike geometry and metallic semi-Riemannian manifolds. [7] Let ðN~ ; ~gÞ be a semi-Riemannian manifold, ðN ; g; SðTN Þ; SðTN ⊥ÞÞ be its r-lightlike submanifold. Eqns (2.4), (2.6) are known as Gauss equations and (2.5), (2.7), (2.8) are known as Weingarten equations respectively, for the lightlike submanifold N of N~. Throughout the paper, we assume that P~ is a locally metallic structure
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