Ricci-corrected derivatives and invariant differential operators

Abstract

We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard invariant operators given in work of Cap, Slovak and Soucek, and at the same time extend these formulae from the context of AHS structures (which include conformal and projective structures) to the more general class of all parabolic structures (including CR structures).

Substantially revised, shortened and simplified, with new treatment of Weyl structures; 24 pages

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Cited by in corpus (17)

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• G2 geometry and integrable systems
• Projectively related metrics, Weyl nullity, and metric projectively invariant equations
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• On automorphism groups of some types of generic distributions
• The BGG Complex on Projective Space
• Branching laws for Verma modules and applications in parabolic geometry. I
• Conformal equations that are not Virasoro or Weyl invariant
• Geometric Theory of Weyl Structures
• Isothermic submanifolds of symmetric $R$-spaces
• Higher symmetries of the conformal powers of the Laplacian on conformally flat manifolds
• Invariant Bilinear Differential Pairings on Parabolic Geometries
• Projective Geometry I: Principles and Properties
• Free $n$-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions
• Bundles of Weyl structures and invariant calculus for parabolic geometries
• Notes on Tractor Calculus
• Möbius-flat hypersurfaces in projective space