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VOL. 16 | 2015 Second Order Symmetries of the Conformal Laplacian
Jean-Philippe Michel, Fabian Radoux, Josef Silhan

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

## 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.

## Information

Published: 1 January 2015
First available in Project Euclid: 13 July 2015

zbMATH: 1350.53092
MathSciNet: MR3363848

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