Induced Semi-Riemannian structures on null submanifolds

TL;DR

This paper develops a method to induce semi-Riemannian metrics on null submanifolds, linking null geometry with classical semi-Riemannian invariants, thereby enhancing understanding of their geometric structure.

Contribution

It introduces a new approach to induce semi-Riemannian metrics on null submanifolds and explores their geometric invariants in relation to the ambient space.

Findings

Established links between null geometry and semi-Riemannian invariants.

Provided a framework for inducing semi-Riemannian metrics on null submanifolds.

Connected null submanifold geometry with ambient semi-Riemannian structures.

Abstract

In this paper, we induce a semi-Riemannian metric on the $r$-null submanifold. We establish the links between the null geometry and basics invariants of the associated semi-Riemannian geometry on $r$-null submanifold and semi-Riemannian constructed from a semi-Riemannian ambient.