Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
Weil bundle; fiber product preserving bundle functor; flow natural map; weak principal connection
Weil bundle; fiber product preserving bundle functor; flow natural map; weak principal connection
Summary:
We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections.
References:
[1] Cabras, A., Kolář, I.: Prolongation of second order connections to vertical Weil bundles. Arch. Math. (Brno) 37 (2001), 333–347. MR 1879456 | Zbl 1090.58003
[2] Cabras, A., Kolář, I.: On the functorial prolongations of principal bundles. Comment. Math. Univ. Carol. 47 (2006), 719–731. MR 2337425 | Zbl 1150.58002
[3] Čap, A., Slovák, J.: Parabolic Geometries I. Mathematical Surveys and Monographs, vol. 154, AMS, Providence, USA, 2009. DOI 10.1090/surv/154/03 | MR 2532439 | Zbl 1183.53002
[4] Kolář, I.: On the geometry of fiber product preserving bundle functors. Differential Geometry and its Applications, Proceedings, Silesian University of Opava, 2002, pp. 63–72. MR 1978765
[5] Kolář, I.: Handbook of Global Analysis. ch. Weil Bundles as Generalized Jet Spaces, pp. 625–664, Elsevier, Amsterdam, 2008. MR 2389643
[6] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, 1993. MR 1202431
[7] Kolář, I., Mikulski, W.M.: On the fiber product preserving bundle functors. Differential Geom. Appl. 11 (1999), 105–115. DOI 10.1016/S0926-2245(99)00022-4 | MR 1712139
[8] Mikulski, W.M.: Fiber product preserving bundle functors as modified vertical Weil functors. 11pp., to appear in Czechoslovak Math. J.
[9] Weil, A.: Théorie des points proches sur les variétes différentielles. Colloque de topol. et géom. diff., Strasbourg , 1953, pp. 111–117. MR 0061455
Search
Partner of
