Lightlike Hypersurfaces of Metallic Semi-Riemannian Manifolds

TL;DR

This paper explores the geometric properties of lightlike hypersurfaces within metallic semi-Riemannian manifolds, focusing on invariant and screen semi-invariant cases, and establishing their structural characteristics and integrability conditions.

Contribution

It introduces the concept of lightlike hypersurfaces in metallic semi-Riemannian manifolds and analyzes their geometric properties and induced structures, which is a novel extension in differential geometry.

Findings

Invariant lightlike hypersurfaces inherit metallic structures.

Conditions for integrability of distributions are established.

Examples illustrating the concepts are provided.

Abstract

In our article, we introduce and study lightlike hypersurfaces of a metallic semi-Riemannian manifold. We examine some geometric properties of invariant lightlike hypersurfaces. We show that the induced structure on an invariant lightlike hypersurface is also metallic. We also define screen semi-invariant lightlike hypersurfaces, investigate integrability conditions for the distributions and give some examples.