PROLONGATION OF SYMMETRIC KILLING TENSORS AND COMMUTING SYMMETRIES OF THE LAPLACE OPERATOR

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Authors	MICHEL Jean-Philippe SOMBERG Petr ŠILHAN Josef
Year of publication	2017
Type	Article in Periodical
Magazine / Source	Rocky Mountain Journal of Mathematics
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1216/RMJ-2017-47-2-587
Keywords	Killing tensors; prolongation of PDEs; commuting symmetries of Laplace operator
Description	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 Riemannian tractor calculus, allowing us to construct a prolongation of the differential system for symmetric Killing tensors. We also discuss some aspects of its relation to projective differential geometry.
Related projects:	Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku