The non-existence of a Lanczos potential for the Weyl curvature tensor in dimensions n>=7

TL;DR

This paper proves that a Lanczos potential for the Weyl curvature tensor cannot exist in spaces of dimension seven or higher, establishing a fundamental limitation in higher-dimensional differential geometry.

Contribution

It demonstrates the non-existence of a Lanczos potential for the Weyl tensor in all spaces with dimension n≥7, a significant theoretical result.

Findings

No Lanczos potential exists for n≥7

The result applies to all spaces of dimension seven or higher

This limits the methods available for studying Weyl curvature in higher dimensions

Abstract

In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension $n\geq 7$.