Curvature actions on Spin(n) bundles

TL;DR

This paper calculates the possible ways curvature tensors can act on irreducible tensor-spinor bundles over Riemannian manifolds, providing a classification of curvature actions in geometric analysis.

Contribution

It explicitly enumerates the independent curvature actions on tensor-spinor bundles, extending understanding of geometric structures in Riemannian geometry.

Findings

Number of independent Weyl-type curvature actions computed

Enumeration of Einstein-type curvature actions provided

Framework for analyzing curvature actions on tensor-spinor bundles established

Abstract

We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of tensors of Einstein type, this enumerates the possible curvature actions on V.