Prolongation of symmetric Killing tensors and commuting symmetries of the Laplace operator

Abstract

We determine the space of commuting sym- metries of the Laplace operator on pseudo-Riemannian man- ifolds of constant curvature and derive its algebra structure. Our construction is based on Riemannian tractor calculus, allowing us to construct a prolongation of the dierential system for symmetric Killing tensors.

We also discuss some aspects of its relation to projective dierential geometry.

Keywords

• Killing tensors
• prolongation of PDEs
• commuting symmetries of Laplace operator