On the torsion of linear higher order connections

• Autorzy: Ivan Kolář
• Języki publikacji: EN

Abstrakty

EN

For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

Słowa kluczowe

EN

linear r-th order connection on the tangent bundle; principal connection on the r-th order frame bundle; torsion; integrability of G-structures; 53C05; 58A20

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 360-366

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Ivan Kolář

• Faculty of Science, Masaryk University

Bibliografia

• [1] A. Cabras and I. Kolář: Flow prolongation of some tangent valued forms, to appear.
• [2] M. Elźanowski and S. Prishepionok: “Connections on higher order frame bundles”, New Developments in Differential Geometry, Proceedings, Kluwer, 1996, pp. 131–142.
• [3] I. Kolář: “Torision free connections on higher order frame bundles”, New Developments in Differential Geometry, Proceedings, Kluwer, 1996, pp. 233–241.
• [4] I. Kolář, P.W. Michor, J. Slovák: Natural Operations in Differential Geometry, Springer-Verlag, 1993, http://www.math.muni.cz/EMIS/monographs/index.html.
• [5] P.C. Yuen: “Higher order frames and linear connections”, Cahiers Topol. Geom. Diff., Vol. 12, (1971), pp. 333–371.
• [6] A. Zajtz: Foundations of Differential Geometry of Natural Bundles, Lecture Notes Univ. Caracas, 1984.

Identyfikatory

DOI

10.2478/BF02475215