Gauree Shanker, Ankit Yadav and Ramandeep Kaur
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…
Abstract
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⊥×λNT 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.
Details
Keywords
On 20 March 2020, the four adult convicts of the 2012 Delhi rape case were executed after a long debate regarding the punishment for their crime. The Delhi rape case, unlike…
Abstract
On 20 March 2020, the four adult convicts of the 2012 Delhi rape case were executed after a long debate regarding the punishment for their crime. The Delhi rape case, unlike others, was also given to the fast track court because of the worldwide outrage India received in its aftermath. Otherwise, most rape survivors rarely speak out and if they do, their lives are often endangered and threatened, depending on the severity of the case itself and the perpetrator's rank in the society. Through the analysis of Aniruddha Roy Chowdhury's, 2016 film Pink, and Ajay Bahl's film Section 375 (2019), this chapter explores the different ways in which mainstream Hindi cinema deals with such questions, especially in its depictions of courts. Both these films foreground India's contemporary cultural systems of fear that silence the rape survivors. They also imply that in the court cases, unless the specific court case faces intense global publicity, as was the case of the Delhi gang rape, rape survivors will never want to speak out. Moreover, the rape survivors will also hesitate to file a First Information Report (FIR) – a document that records crimes by the police against their perpetrators – limiting any possibility for justice for them. The laws surrounding rape cases are obscure and complex and finding justice for a rape victim (unless it is on a global level) is not an easy venture in India. At the time of the #metoo movement, the rape laws in India are not designed in such a way to arguably encourage victim-survivors to speak up. Instead, if rape survivors do decide to confront their perpetrators, they not only face ostracisation from society but also the danger of losing loved ones and endanger their lives as well.