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

Josef Janyška; Marco Modugno

Archivum Mathematicum (1996)

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

Abstract

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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).

How to cite

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Janyška, 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

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  1. 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
  2. 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) 
  3. A. Jadczyk M. Modugno, Galilei general relativistic quantum mechanics, book manuscript, 1994. (1994) Zbl1004.83518
  4. I. Kolář P. W. Michor J. Slovák, Natural Operations in Differential Geometry, Springer–Verlag, 1993. (1993) Zbl0782.53013MR1202431
  5. D. Krupka J. Janyška, Lectures on Differential Invariants, Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990. (1990) Zbl0752.53004MR1108622
  6. L. Mangiarotti M. Modugno, Connections and differential calculus on fibred manifolds, Istituto di Matematica Applicata “G. Sansone”, Università di Firenze, 1989. (1989) Zbl0841.53023
  7. A. Nijenhuis, Natural bundles and their general properties, Diff. Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, pp. 317–334. (1972) Zbl0246.53018MR0380862
  8. 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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