Screen Generic Lightlike Submanifolds of a Locally Bronze Semi-Riemannian Manifold equipped with an (l,m)-type Connection

TL;DR

This paper explores the geometry of screen generic lightlike submanifolds within locally bronze semi-Riemannian manifolds, providing characterization theorems, non-existence results, and examples of minimal submanifolds.

Contribution

It introduces the geometry of these submanifolds with an (l,m)-type connection, including new theorems on geodesicity, non-existence results, and structure analysis with examples.

Findings

No coisotropic, isotropic, or totally proper screen generic lightlike submanifolds exist in such manifolds.

Characterization theorems relate geodesicity to distribution properties.

Examples of minimal screen generic lightlike submanifolds are provided.

Abstract

The present paper introduces the geometry of screen generic lightlike submanifolds of a locally bronze semi-Riemannian manifolds endowed with an (l,m)-type connection. The characterization theorems on geodesicity of such submanifolds with respect to the integrability and parallelism of the distributions are provided. It is proved that there exists no coisotropic , isotropic or totally proper screen generic lightlike submanifold of a locally bronze semi-Riemannian manifold. Assertions for the smooth transversal vector fields in totally umbilical proper screen generic lightlike submanifold are obtained. The structure of a minimal screen generic lightlike submanifold of a locally bronze semi-Riemannian manifold is detailed with an example.