Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the generalized Ferrand–Obata theorem proved by C. Frances, this proves a generali...

Infinitesimal conformal transformations of IRn are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over IRn, n ≥ 2, is maximal in the Lie algebra of polynomial vector fields. When n is greater than 2 and p, q are such that p+ q = n, this implies the maximality of an embedding of so(p + 1, q + 1, IR) in...

We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g) admitting a conformal contact quasi-torse-forming vector field T . The presymplectic 2-form Ω is a locally conformal cosymplectic 2-form. It is shown that T is a 3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated. The Gauss map of the hypersurfaceMξ normal to ξ is conforma...

We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on even-dimensional conformal manifolds. The exposition is self-contained, in the sense of giving references sufficient to allow the reader to work through all ...

Abstract. We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to th...