Killing spinor-valued forms and the cone construction

TL;DR

This paper introduces Killing-type equations for spinor-valued forms on pseudo-Riemannian manifolds and explores their connection to parallel fields on the metric cone, advancing understanding of geometric structures related to spinors.

Contribution

It formulates new Killing equations for spinor-valued forms and analyzes their solutions in relation to parallel fields on metric cones, providing novel insights into geometric analysis.

Findings

Killing equations for spinor-valued forms are established.

Solutions relate to parallel fields on the metric cone.

The study enhances understanding of geometric structures involving spinors.

Abstract

On a pseudo-Riemannian manifold $\mathcal{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathcal{M}$ and parallel fields on the metric cone over $\mathcal{M}$ for spinor-valued forms.