# Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold

Archivum Mathematicum (1996)

- Volume: 032, Issue: 4, page 281-288
- ISSN: 0044-8753

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topJanyška, Josef, and Modugno, Marco. "Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold." Archivum Mathematicum 032.4 (1996): 281-288. <http://eudml.org/doc/18470>.

@article{Janyška1996,

abstract = {All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).},

author = {Janyška, Josef, Modugno, Marco},

journal = {Archivum Mathematicum},

keywords = {tangent bundle; jet bundle; connection; natural operator; tangent bundle; jet bundle; connection; natural operator},

language = {eng},

number = {4},

pages = {281-288},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold},

url = {http://eudml.org/doc/18470},

volume = {032},

year = {1996},

}

TY - JOUR

AU - Janyška, Josef

AU - Modugno, Marco

TI - Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold

JO - Archivum Mathematicum

PY - 1996

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 032

IS - 4

SP - 281

EP - 288

AB - All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).

LA - eng

KW - tangent bundle; jet bundle; connection; natural operator; tangent bundle; jet bundle; connection; natural operator

UR - http://eudml.org/doc/18470

ER -

## References

top- D. Canarutto A. Jadczyk M. Modugno, Quantum mechanics of a spin particle in a curved spacetime with absolute time, Rep. on Math. Phys., 36, 1 (1995), 95–140. (1995) Zbl0888.53052MR1377229
- A. Jadczyk M. Modugno, An outline of a new geometric approach to Galilei general relativistic quantum mechanics, in C.N. Yang, M.L. Ge and X. W. Zhou editors, Proc. XXI Int. Conf. on Differential geometric methods in theoretical physics, Tianjin 5-9 June 1992, 543-556, Singapore, 1992, World Scientific. (1992)
- A. Jadczyk M. Modugno, Galilei general relativistic quantum mechanics, book manuscript, 1994. (1994) Zbl1004.83518
- I. Kolář P. W. Michor J. Slovák, Natural Operations in Differential Geometry, Springer–Verlag, 1993. (1993) Zbl0782.53013MR1202431
- D. Krupka J. Janyška, Lectures on Differential Invariants, Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990. (1990) Zbl0752.53004MR1108622
- L. Mangiarotti M. Modugno, Connections and differential calculus on fibred manifolds, Istituto di Matematica Applicata “G. Sansone”, Università di Firenze, 1989. (1989) Zbl0841.53023
- A. Nijenhuis, Natural bundles and their general properties, Diff. Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, pp. 317–334. (1972) Zbl0246.53018MR0380862
- J. Slovák, On the finite order of some operators, Proc. Conf. Diff. Geom. and Its Appl. (communications), Brno 1986, Published by J. E. Purkyně University 1987, 283-294. (1986) Zbl0629.58001MR0923390

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