A Weyl-covariant tensor calculus

TL;DR

This paper develops a tensor calculus framework on (pseudo-) Riemannian manifolds that is covariant under Weyl rescalings, introducing a Weyl-covariant operator and related geometric structures using BRST methods.

Contribution

It constructs a Weyl-covariant tensor calculus and operator D, providing new tools for conformal geometry analysis on manifolds.

Findings

Defined a space of Weyl-covariant tensors.

Introduced a Weyl-covariant operator D with specific curvature relations.

Derived transformation laws for generalized connections.

Abstract

On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl rescalings are also derived. These results are obtained by application of BRST techniques.