Geodesic
Cartan Connections and Lie Algebroids
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009)

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This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A. D., Trans. Amer. Math. Soc. 358 (2006), 3651–3671], and tractor calculus [Čap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001), 1511–1548].
Keywords: adjoint tractor bundle; algebroid connection; algebroid representation; Cartan connection; Cartan geometry; Lie algebroid; tractor calculus. 
Michael Crampin. Cartan Connections and Lie Algebroids. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a60/
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[1] Blaom A. D., “Geometric structures as deformed infinitesimal symmetries”, Trans. Amer. Math. Soc., 358 (2006), 3651–3671 ; math.DG/0404313 | DOI | MR | Zbl

[2] Čap A., “Infinitesimal automorphisms and deformations of parabolic geometries”, J. Eur. Math. Soc. (JEMS), 10 (2008), 415–437 ; math.DG/0508535 | MR

[3] Čap A., Gover A. R., “Tractor calculi for parabolic geometries”, Trans. Amer. Math. Soc., 354 (2001), 1511–1548 | MR

[4] Sharpe R. W., Differential geometry. Cartan's generalization of Klein's Erlangen program, with a foreword by S. S. Chern, Graduate Texts in Mathematics, 166, Springer-Verlag, New York, 1997 | MR | Zbl