# On the torsion of linear higher order connections

Open Mathematics (2003)

- Volume: 1, Issue: 3, page 360-366
- ISSN: 2391-5455

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topIvan Kolář. "On the torsion of linear higher order connections." Open Mathematics 1.3 (2003): 360-366. <http://eudml.org/doc/268897>.

@article{IvanKolář2003,

abstract = {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.},

author = {Ivan Kolář},

journal = {Open Mathematics},

keywords = {53C05; 58A20},

language = {eng},

number = {3},

pages = {360-366},

title = {On the torsion of linear higher order connections},

url = {http://eudml.org/doc/268897},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Ivan Kolář

TI - On the torsion of linear higher order connections

JO - Open Mathematics

PY - 2003

VL - 1

IS - 3

SP - 360

EP - 366

AB - 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.

LA - eng

KW - 53C05; 58A20

UR - http://eudml.org/doc/268897

ER -

## References

top- [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. Zbl0851.58003
- [3] I. Kolář: “Torision free connections on higher order frame bundles”, New Developments in Differential Geometry, Proceedings, Kluwer, 1996, pp. 233–241. Zbl0901.53016
- [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. Zbl0782.53013
- [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.