Higher Symmetries of the conformal Laplacian

Conference (2014, July 14)

SECOND ORDER SYMMETRIES OF THE CONFORMAL LAPLACIAN

in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2014), 10(016), 26

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 ... [more ▼]

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 differential 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. [less ▲]

Quantifications équivariantes

Scientific conference (2013, November 05)

Higher symmetries of the conformal Laplacian

Conference (2013, May 29)

spo(2|2)-equivariant quantizations on the supercircle S^{1|2}

in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2013), 9(055), 17

On osp(p+1,q+1|2r)-equivariant quantizations

in Journal of Geometry & Physics (2012), 62

Projectively equivariant quantization over R^{p|q}

Conference (2011, September 13)

Quantifications équivariantes

Scientific conference (2011, April 15)

Natural and Projectively Invariant Quantizations on Supermanifolds

in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2011)

The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using ... [more ▼]

The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two. [less ▲]

Quantifications équivariantes

Scientific conference (2011, January 27)