# On the embedding of Weyl manifolds

## TL;DR

This paper explores extending the Campbell-Magaard embedding theorem to Weyl manifolds, revealing both possibilities and challenges, and establishing new no-go theorems relevant to higher-dimensional theories.

## Contribution

It generalizes known embedding results to Weyl geometry and identifies new difficulties and no-go theorems specific to this setting.

## Key findings

- Some known embedding results extend to Weyl geometry.
- New no-go theorems restrict embedding possibilities.
- Highlights challenges due to Weylian geometric properties.

## Abstract

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known results can be naturally extended to the new geometric scenario, although new difficulties arise. In pursuit of solving the embedding problem we have obtained some no-go theorems. We also highlight some of the difficulties that appear in the embedding problem, which are typical of the Weylian character of the geometry. The establishing of these new results may be viewed as part of a program that highlights the possible significance of embedding theorems of increasing degrees of generality in the context of modern higher-dimensional space-time theories.