Let (M, g) be a pseudo-Riemannian manifold and Fλ(M) the space of densities of degree λ on M . We study the space D2 λ,μ(M) of second-order differential operators from Fλ(M) to Fμ(M). If (M, g) is conformally flat with signature p− q, then D2 λ,μ(M) is viewed as a module over the group of conformal transformations of M . We prove that, for almost all values of μ− λ, the O(p+1, q+1)-modules D2 λ...

Using the conformal invariance of the SL(2, IR) ⊗ SO(1, 1) d−2 /SO(1, 1) coset models we calculate the conformally exact metric and dilaton, to all orders in the 1/k expansion. We consider both vector and axial gauging. We find that these cosets represent two different space–time geometries: (2d black hole)⊗IR d−2 for the vector gauging and (3d black string)⊗IR d−3 for the axial one. In particu...

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally recurrent manifold is shown to be either a de Sitter space or an anti-de space. In particular, spacetime must spacetime.