Tractor calculi for parabolic geometries

By Andreas Čap, A. Gover. 2001

190 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f86c0b7e93b1b1e40ff4ec329c43b26a8a43ec77

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In Geometry and Topology

1. C. Graham
2. A. Gover
3. Andreas Čap
4. D. Calderbank
5. F. Burstall
6. Anthony D. Blaom
7. T. Diemer
8. R. Myers

In Mathematical Physics

1. C. Graham
2. D. Calderbank
3. Andreas Čap
4. A. Gover
5. T. Diemer
6. Anthony D. Blaom

Citations in the corpus

• Conformal submanifold geometry I-III (2010, background): “Such vector bundles with connection, induced by a Cartan connection, are now called tractor bundles or (local) twistor bundles [3, 4, 29].”
• Higher symmetries of the laplacian (2002, unknown): “This extends (5) to the curved setting.”
• Geometric structures as deformed infinitesimal symmetries (2004, background): “This appears to be closely related to the so-called ‘tractor’ or ‘local twistor’ calculus used in conformal geometry [4].”
• Infinitesimal automorphisms and deformations of parabolic geometries (2005, background): “Finally, the fundamental derivative was introduced under the name of “fundamental D-operator” in Section 3 of [8].”
• Correspondence spaces and twistor spaces for parabolic geometries (2001, background): “Let V be a representation of G, and for any parabolic geometry (p : G → M, ω) consider the natural vector bundle V M := G × P V. Bundles of that type are called tractor bundles, see [5].”
• Ricci-corrected derivatives and invariant differential operators (2003, unknown): “In this section, we recall the basic calculus of such geometries, following [10] [12] [22] [32] [33].”
• CR invariant powers of the sub-Laplacian (2003, methodology): “n-Moser, but we found it preferable to proceed directly, especially POWERS OF THE SUB-LAPLACIAN 3 for the tractor Dcalculus needed for the construction of the invariant operators. See [1], [9], [17], [4] for further discussion and background about tractors. Given this machinery, the construction of ”
• CR-Tractors and the Fefferman Space (2006, methodology): “7 of [8], the difference D̃JD̃sφ−D̃sD̃Jφ is given by D̃[J,s]φ, where [J, s] denotes the Lie bracket of the two adjoint tractor fields.”
• Two constructions with parabolic geometries (2005, unknown): “This leads to the so–called tractor bundles, see [1] [10].”
• Di erential invariants and curved Bernstein-Gelfand-Gelfand sequences (2000, background): “The same idea appears in [14, 39], the latter reference attributing it to Cartan [13].”
• Conformally invariant powers of the Laplacian — A complete nonexistence theorem (2004, unknown): “It is intimately related to the Cartan conformal connection; for a comprehensive treatment exposing this connection and relating the conformal case to the wider setting of parabolic structures see [ 4 , 3]. The calculational techniques, conventions and notation used here follow [12] and [10].”