Ricci-corrected derivatives and invariant differential operators

By D. Calderbank, T. Diemer, V. Souček. 2003

53 citations recorded by the source corpus.

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 [A. Cap, J. Slovak, V. Soucek, Invariant operators on manifolds with almost hermitian symmetric structures, III. Standard operators, Differential Geom. Appl. 12 (2000) 51–84], 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).

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bf77491e78e404b31a02d27675714996fe3f0eee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. F. Burstall
2. D. Calderbank

In Astronomy and Astrophysics

1. F. Burstall
2. D. Calderbank
3. Andreas Čap
4. Michael Eastwood

In Geometry and Topology

1. F. Burstall
2. D. Calderbank

Citations in the corpus

• Conformal submanifold geometry I-III (2010, background): “A Cartan connection in the usual sense (see [26, 70]), modelled on a homogeneous space G/P , is a principal G-bundle C equipped with a principal G-connection ω and a reduction G ⊂ C to a principal P -bundle such that ω|G mod p : TG → g/p is an isomorphism on each tangent space.”