Killing spinor-valued forms and their integrability conditions

Abstract

We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the pointwise values of solutions to the curvature of the underlying manifold.

As an example, we completely solve the equations on model spaces of constant curvature producing brand-new solutions which do not come from the tensor product of Killing spinors and Killing-Yano forms.

Keywords

• Killing-type equations
• Prolongation of differential systems
• Projective invariance
• Spinor-valued differential forms
• Cone construction
• Constant curvature space