Second Order Symmetries of the Conformal Laplacian
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Symmetry, Integrability and Geometry: Methods and Applications |
| MU Faculty or unit | |
| 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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