Transversal Lightlike Submanifolds of Metallic Semi-Riemannian Manifolds

TL;DR

This paper explores the geometry of transversal lightlike submanifolds within Metallic semi-Riemannian manifolds, providing conditions for metric connections and characterizations, along with an illustrative example.

Contribution

It introduces new geometric characterizations of transversal lightlike submanifolds in Metallic semi-Riemannian manifolds and analyzes conditions for induced metric connections.

Findings

Derived necessary and sufficient conditions for metric connections.

Characterized transversal lightlike submanifolds in this context.

Provided an explicit example illustrating the concepts.

Abstract

The Metallic Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Metallic structure will be called a Metallic Riemannian manifold. The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds and of Metallic Semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterization of transversal lightlike submanifolds of Metallic semi-Riemannian manifolds. Finally, we give an example.