Ricci-corrected derivatives and invariant differential operators

Details Ricci-corrected derivatives and invariant differential operators Ricci-corrected derivatives and invariant differential operators

2003-10-20

arxiv.org/abs/math/0310311v2

Diff. Geom. Appl. 23 (2005) 149-175.

Mathematics

Differential Geometry

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

Scientific paper

10.1016/j.difgeo.2004.07.009

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).

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