Projectively and Conformally Invariant Star-Products

00 5 Projectively Invariant Star Products

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the one constructed previ...

O ct 2 00 5 PROJECTIVELY INVARIANT STAR PRODUCTS

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth functions on the cotangent bundle, fiberwise-polynomial of bounded degree, a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the on...

Is mass conformally invariant ?

By using the Garfinkle, Horowitz and Strominger black hole solutions as examples, we illustrate that, with respect to the reference action functional proposed by Hawking and Horowitz, the asymp-totic mass parameter is not invariant between two conformally related static spherically symmetric metrics.

Minimization of Conformally Invariant Energies

Conformally Invariant Non-local Operators

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...