Killing spinor-valued forms and the cone construction

Abstract

On a pseudo-Riemannian manifold $\mathbb{M}$ 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 $\mathbb{M}$ and parallel fields on the metric cone over $\mathbb{M}$ for spinor-valued forms.

Keywords

• pseudo-Riemannian spin manifolds
• Killing type equations
• cone construction
• spinor-valued differential forms