Killing tensor spinor forms and their application in Riemannian geometry

Abstract

We introduce the notion of Killing tensor spinor forms as a generalization of Killing forms in Riemannian geometry. In the case of spinor valued forms, the analysis is based on the technique of Howe dual pairs.

As an application we show that Killing tensor spinors yield invariants of geodesics of the underlying Riemannian manifold.

Keywords

• Riemannian and conformal geometry
• Killing spinor forms
• Killing tensor spinors
• geodesic