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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.