Lightlike Submanifolds of Metallic Semi-Riemannian Manifolds

TL;DR

This paper explores specific lightlike submanifolds within metallic semi-Riemannian manifolds, analyzing their geometric properties, conditions for metric connections, and integrability of distributions, with illustrative examples.

Contribution

It introduces new classifications of lightlike submanifolds in metallic semi-Riemannian manifolds and establishes conditions for their geometric structures.

Findings

Conditions for the induced connection to be metric are derived.

Necessary and sufficient conditions for distribution integrability are provided.

Examples illustrating the theoretical results are presented.

Abstract

Our aim in this paper is to investigate some types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifolds and give examples. We obtain the conditions for the induced connection to be a metric connection. Also, we find necessary and sufficient conditions for the distributions involved in the definitions of such submanifolds to be integrable.