On the Geometry of Lightlike Submanifolds in Metallic Semi-Riemannian Manifolds

TL;DR

This paper explores the geometric properties of lightlike submanifolds within metallic semi-Riemannian manifolds, classifying various subclasses and establishing conditions for their geometric features and existence.

Contribution

It introduces new subclasses of lightlike submanifolds in metallic semi-Riemannian manifolds and provides conditions for their geometric properties and non-existence results.

Findings

Certain subclasses do not exist in this setting.

Conditions for the induced connection to be metric are established.

Criteria for isotropic submanifolds to be totally geodesic are given.

Abstract

In the present paper, we introduce screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds with its subclasses, namely screen transversal anti-invariant, radical screen transversal and isotropic screen transversal lightlike submanifolds, and give an example. We show that there do not exist co-isotropic and totally screen transversal type of screen transversal anti-invariant lightlike submanifolds of a metallic semi-Riemannian manifold. We investigate the geometry of distributions involved in the definition of such submanifolds and the conditions for the induced connection to be a metric connection. Furthermore, we give a necessary and sufficient condition for an isotropic screen transversal lightlike submanifold to be totally geodesic.