Geometric realizations, curvature decompositions, and Weyl manifolds

TL;DR

This paper demonstrates that any algebraic model of Weyl curvature can be represented by an actual Weyl manifold, bridging the gap between abstract models and geometric realizations.

Contribution

It establishes a universal realization result for Weyl curvature models within the framework of Weyl manifolds.

Findings

Any Weyl curvature model can be geometrically realized by a Weyl manifold.

Provides a constructive approach for realizing algebraic curvature models.

Enhances understanding of the relationship between algebraic and geometric structures in Weyl geometry.

Abstract

We show any Weyl curvature model can be geometrically realized by a Weyl manifold