Publication details

Second Order Symmetries of the Conformal Laplacian

Authors

ŠILHAN Josef MICHEL Jean-Philippe RADOUX Fabian

Year of publication 2014
Type Article in Periodical
Magazine / Source Symmetry, Integrability and Geometry: Methods and Applications
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.3842/SIGMA.2014.016
Field General mathematics
Keywords Laplacian; quantization; conformal geometry; separation of variables
Description Let (M;g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M;g), which are given by dif ferential operators of second order. They are constructed from conformal Killing 2-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. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two families of examples in dimension three
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