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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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 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.

Article information

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

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502552

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-587

Mathematical Reviews number (MathSciNet)
MR3635376

Zentralblatt MATH identifier
1371.35034

Subjects
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]

Keywords
Killing tensors prolongation of PDEs commuting symmetries of Laplace operator

Citation

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. https://projecteuclid.org/euclid.rmjm/1492502552


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