• Corpus ID: 40420678

INVARIANT OPERATORS OF THE FIRST ORDER ON MANIFOLDS WITH A GIVEN PARABOLIC STRUCTURE

@inproceedings{Slovk2000INVARIANTOO,
  title={INVARIANT OPERATORS OF THE FIRST ORDER ON MANIFOLDS WITH A GIVEN PARABOLIC STRUCTURE},
  author={Jan Slov{\'a}k and Vladim{\'i}r Sou{\vc}ek},
  year={2000}
}

• J. Slovák, V. Souček
• Published 2000
• Mathematics

The goal of this paper is to describe explicitly all invariant first order operators on manifolds equipped with parabolic geometries. Both the results and the methods present an essential generalization of Fegan's description of the first order invariant operators on conformal Riemannian manifolds. On the way to the results, we present a short survey on basic structures and properties of parabolic geometries, together with links to further literature. Resume (Operateurs invariants d'ordre 1 sur des varietes paraboliques). — Le but de l'ar- ticle est de decrire explicitement tous les operateurs differentiels invariants d'ordre un sur les varietes munies d'une structure de geometrie parabolique (les espaces gene- ralises d' ´ Elie Cartan). Les resultats, ainsi que les methodes, generalisent un resultat de Fegan sur la classification des operateurs differentiels d'ordre un sur une variete munie d'une structure conforme. Au passage, nous donnons un bref resumed es pro- prietes fondamentales des espaces generalises d' ´ E. Cartan et du calcul differentiel sur