Publication details

SECOND ORDER SYMMETRIES OF THE CONFORMAL LAPLACIAN

Authors

MICHEL Jean-Philippe RADOUX Fabian ŠILHAN Josef

Year of publication 2015
Type Article in Proceedings
Conference PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON GEOMETRY, INTEGRABILITY AND QUANTIZATION
MU Faculty or unit

Faculty of Science

Citation
Web https://projecteuclid.org/download/pdf_1/euclid.pgiq/1436815747
Doi http://dx.doi.org/10.7546/giq-16-2015-231-249
Keywords Laplacian; Quantization; Conformal geometry; separation of variables
Description Let (M, 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, 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.
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