The constructions of general connections on second jet prolongation

Mariusz Plaszczyk

Annales UMCS, Mathematica (2014)

  • Volume: 68, Issue: 1, page 67-89
  • ISSN: 2083-7402

Abstract

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We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M

How to cite

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Mariusz Plaszczyk. "The constructions of general connections on second jet prolongation." Annales UMCS, Mathematica 68.1 (2014): 67-89. <http://eudml.org/doc/267169>.

@article{MariuszPlaszczyk2014,
abstract = {We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M},
author = {Mariusz Plaszczyk},
journal = {Annales UMCS, Mathematica},
keywords = {General connection; classical linear connection; higher order jet prolongation; bundle functor; natural operator; general connection},
language = {eng},
number = {1},
pages = {67-89},
title = {The constructions of general connections on second jet prolongation},
url = {http://eudml.org/doc/267169},
volume = {68},
year = {2014},
}

TY - JOUR
AU - Mariusz Plaszczyk
TI - The constructions of general connections on second jet prolongation
JO - Annales UMCS, Mathematica
PY - 2014
VL - 68
IS - 1
SP - 67
EP - 89
AB - We determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M
LA - eng
KW - General connection; classical linear connection; higher order jet prolongation; bundle functor; natural operator; general connection
UR - http://eudml.org/doc/267169
ER -

References

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  1. [1] Doupovec, M., Mikulski, W., Holonomic extension of connections and symmetrization of jets, Rep. Math. Phys. 60 (2007), 299-316.[WoS] Zbl1160.58001
  2. [2] Ehresmann, C., Sur les connexions d’ordre sup´erieur, Atti del V. Cong. del’Unione Mat. Italiana, 1955, Cremonese, Roma, 1956, 344-346. 
  3. [3] Kolář, I., Higher order absolute differentiation with respect to generalized connections, Differential Geometry, Banach Center Publ. 12, PWN-Polish Sci. Publ., Warszawa, 1984, 153-162. 
  4. [4] Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. Zbl0782.53013
  5. [5] Kolář, I., Prolongations of generalized connections, Differential Geometry (Budapest, 1979), Colloq. Math. Soc. János Bolyai, 31, North-Holland, Amsterdam, 1982, 317-325. 
  6. [6] Kolář, I., On the torsion free connections on higher order frame bundles, New Developments in Differential Geometry (Debrecen, 1994), Proceedings (Conference in Debrecen), Math. Appl., 350, Kluwer Acad. Publ., Dordrecht, 1996, 233-241. Zbl0901.53016
  7. [7] Kurek, J., Mikulski, W., On prolongations of projectable connections, Ann. Polon. Math. 101 (2011), no. 3, 237-250. Zbl1230.58007
  8. [8] Mikulski, W., On “special” fibred coordinates for general and classical connections, Ann. Polon. Math. 99 (2010), 99-105.[WoS] Zbl1217.58003
  9. [9] Mikulski, W., Higher order linear connections from first order ones, Arch. Math. (Brno) 43 (2007), 285-288. Zbl1164.58001

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