Subtleties concerning conformal tractor bundles

• Autorzy: C. Graham , Travis Willse
• Języki publikacji: EN

Abstrakty

EN

The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and equivalence between parabolic geometries and underlying structures.

Słowa kluczowe

EN

Conformal geometry; Parabolic geometry; Tractor bundle; Cartan connection; Associated bundle

Kategorie tematyczne

• 53A30: Conformal differential geometry

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1721-1732

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

C. Graham

• University of Washington

autor

Travis Willse

• The Australian National University

Bibliografia

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• [2] Čap A., Gover A.R., Tractor calculi for parabolic geometries, Trans. Amer. Math. Soc., 2002, 354(4), 1511–1548 http://dx.doi.org/10.1090/S0002-9947-01-02909-9
• [3] Čap A., Gover A.R., Standard tractors and the conformal ambient metric construction, Ann. Global Anal. Geom., 2003, 24(3), 231–259 http://dx.doi.org/10.1023/A:1024726607595
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• [8] Fefferman C., Graham C.R., The Ambient Metric, Ann. of Math. Stud., 178, Princeton University Press, Princeton, 2012
• [9] Graham C.R., Willse T., Parallel tractor extension and ambient metrics of holonomy split G 2, J. Diff. Geom. (in press), preprint available at http://arxiv.org/abs/1109.3504
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Identyfikatory

DOI

10.2478/s11533-012-0093-8