  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 generalization of the "Lichnerowicz conjecture" for conformal
Riemannian, strictly pseudo-convex CR, and quaternionic/octonionic contact
manifolds in positive-definite signature. For an infinitesimal automorphism
with a singularity, we give a generalization of the dictionary introduced by
Frances for conformal Killing fields, which characterizes (local) essentiality
via the so-called holonomy associated to a singularity of an infinitesimal
automorphism.
