Rocky Mountain Journal of Mathematics

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

Jean-Philippe Michel, Petr Somberg, and Josef Šilhan

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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.

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Rocky Mountain J. Math., Volume 47, Number 2 (2017), 587-619.

First available in Project Euclid: 18 April 2017

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Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35R01: Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] 53A20: Projective differential geometry 58J70: Invariance and symmetry properties [See also 35A30]

Killing tensors prolongation of PDEs commuting symmetries of Laplace operator


Michel, Jean-Philippe; Somberg, Petr; Šilhan, Josef. Prolongation of symmetric Killing tensors and commuting symmetries of the Laplace operator. Rocky Mountain J. Math. 47 (2017), no. 2, 587--619. doi:10.1216/RMJ-2017-47-2-587.

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