This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the C...

We give an algebraic characterization of the case when conformal Weyl and conformal Lyra connections have the same curvature tensor. It is determined a (1,3)-tensor field invariant to certain transformation of semi-symmetric connections, compatible with Weyl structures on conformal manifolds. It is studied the case when this tensor is vanishing. M.S.C. 2000: 53B05, 53B20, 53B21.

Ergodic properties of rational maps are studied, generalising the work of F. Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for an ergodic invariant probability measure with positive Lyapunov exponent to be absolutely continuous with respect to a general conformal measure. If they hold...

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a group-invariant metric and connection, and serves as the model space for a new conformal gauge theory. ∗Electronic-mail: [email protected]

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace-Beltrami operator covariant under conformal transformations, the other to the naive non invariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regular...

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...