1. Prolongation of symmetric Killing tensors and commuting symmetries of the Laplace operator
- Author
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Petr Somberg, Josef Šilhan, and Jean-Philippe Michel
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Algebraic structure ,58J70 ,General Mathematics ,53A20 ,Space (mathematics) ,Differential systems ,01 natural sciences ,35J05 ,0103 physical sciences ,FOS: Mathematics ,prolongation of PDEs ,Projective differential geometry ,0101 mathematics ,commuting symmetries of Laplace operator ,35R01 ,Mathematics ,010308 nuclear & particles physics ,010102 general mathematics ,Prolongation ,35R01, 53A20, 58J70, 35J05 ,Constant curvature ,Differential Geometry (math.DG) ,Homogeneous space ,Killing tensors ,Mathematics::Differential Geometry ,Laplace operator - Abstract
We determine the space of commuting symmetries of the Laplace operator on pseudo-Riemannian manifolds of constant curvature, and derive its algebra structure. Our construction is based on the Riemannian tractor calculus, allowing to construct a prolongation of the differential system for symmetric Killing tensors. We also discuss some aspects of its relation to projective differential geometry., 21 pages
- Published
- 2014