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2012 | 10 | 5 | 1721-1732
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Subtleties concerning conformal tractor bundles

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
5
Strony
1721-1732
Opis fizyczny
Daty
wydano
2012-10-01
online
2012-07-24
Twórcy
autor
Bibliografia
  • [1] Bailey T.N., Eastwood M.G., Gover A.R., Thomas’s structure bundle for conformal, projective and related structures, Rocky Mountain J. Math., 1994, 24(4), 1191–1217 http://dx.doi.org/10.1216/rmjm/1181072333
  • [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
  • [4] Čap A., Schichl H., Parabolic geometries and canonical Cartan connections, Hokkaido Math. J., 2000, 29(3), 453–505
  • [5] Čap A., Slovák J., Parabolic Geometries I, Math. Surveys Monogr., 154, American Mathematical Society, Providence, 2009
  • [6] Čap A., Slovák J., Souček V., Bernstein-Gelfand-Gelfand sequences, Ann. of Math., 2001, 154(1), 97–113 http://dx.doi.org/10.2307/3062111
  • [7] Fefferman C., Graham C.R., Conformal invariants, In: The Mathematical Heritage of Élie Cartan, Lyon, 1984, Astérisque, 1985, Numero Hors Serie, 95–116
  • [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
  • [10] Hammerl M., Sagerschnig K., Conformal structures associated to generic rank 2 distributions on 5-manifolds - characterization and Killing-field decomposition, SIGMA Symmetry Integrability Geom. Methods Appl., 2009, 5, #081
  • [11] Morimoto T., Geometric structures on filtered manifolds, Hokkaido Math. J., 1993, 22(3), 263–347
  • [12] Nurowski P., Differential equations and conformal structures, J. Geom. Phys., 2005, 55(1), 19–49 http://dx.doi.org/10.1016/j.geomphys.2004.11.006
  • [13] Sharpe R.W., Differential Geometry, Grad. Texts in Math., 166, Springer, New York, 1997
  • [14] Tanaka N., On the equivalence problems associated with simple graded Lie algebras, Hokkaido Math. J., 1979, 8(1), 23–84
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0093-8
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