## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Second Order Symmetries of the Conformal Laplacian

#### Abstract

Let $(M,{\rm g})$ be an arbitrary pseudo-Riemannian manifold of dimension at least three. We determine the form of all the conformal symmetries of the conformal Laplacian on $(M,{\rm g})$, which are given by differential operators of second order. They are constructed from conformal Killing two-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. We illustrate our results on two families of examples in dimension three. Besides, we explain how the (conformal) symmetries can be used to characterize the $R$-separation of some PDEs.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436815747

Digital Object Identifier
doi:10.7546/giq-16-2015-231-249

Mathematical Reviews number (MathSciNet)
MR3363848

Zentralblatt MATH identifier
1350.53092

#### Citation

Michel, Jean-Philippe; Radoux, Fabian; Silhan, Josef. Second Order Symmetries of the Conformal Laplacian. Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization, 231--249, Avangard Prima, Sofia, Bulgaria, 2015. doi:10.7546/giq-16-2015-231-249. https://projecteuclid.org/euclid.pgiq/1436815747