The constructions of general connections on the fibred product of q copies of the first jet prolongation
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2018)
- Volume: 72, Issue: 1
- ISSN: 0365-1029
Access Full Article
top
Abstract
topHow to cite
topMariusz Plaszczyk. "The constructions of general connections on the fibred product of q copies of the first jet prolongation." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 72.1 (2018): null. <http://eudml.org/doc/290764>.
@article{MariuszPlaszczyk2018,
abstract = {We describe all natural operators $A$ transforming general connections $\Gamma $ on fibred manifolds $Y \rightarrow M$ and torsion-free classical linear connections $\Lambda $ on $M$ into general connections $A(\Gamma ,\Lambda )$ on the fibred product $J^\{\}Y \rightarrow M$ of $q$ copies of the first jet prolongation $J^\{1\}Y \rightarrow M$.},
author = {Mariusz Plaszczyk},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {General connection; classical linear connection; first jet prolongation; bundle functor; natural operator},
language = {eng},
number = {1},
pages = {null},
title = {The constructions of general connections on the fibred product of q copies of the first jet prolongation},
url = {http://eudml.org/doc/290764},
volume = {72},
year = {2018},
}
TY - JOUR
AU - Mariusz Plaszczyk
TI - The constructions of general connections on the fibred product of q copies of the first jet prolongation
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2018
VL - 72
IS - 1
SP - null
AB - We describe all natural operators $A$ transforming general connections $\Gamma $ on fibred manifolds $Y \rightarrow M$ and torsion-free classical linear connections $\Lambda $ on $M$ into general connections $A(\Gamma ,\Lambda )$ on the fibred product $J^{}Y \rightarrow M$ of $q$ copies of the first jet prolongation $J^{1}Y \rightarrow M$.
LA - eng
KW - General connection; classical linear connection; first jet prolongation; bundle functor; natural operator
UR - http://eudml.org/doc/290764
ER -
References
top- Doupovec, M., Mikulski, W. M., Holonomic extension of connections and symmetrization of jets, Rep. Math. Phys. 60 (2007), 299-316.
- Kolar, I., Prolongations of generalized connections, in: Differential Geometry (Budapest,1979), Colloq. Math. Soc. Janos Bolyai, 31, North-Holland, Amsterdam, 1982, 317-325.
- Kolar, I., Higher order absolute differentiation with respect to generalized connections, in: Differential Geometry (Warsaw, 1979), PWN – Polish Sci. Publ., Warszawa, 1984, 153-162.
- Kolar, I., Michor, P. W., Slovak J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
- Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math. 101 (3) (2011), 237-250.
- Mikulski, W. M., On “special” fibred coordinates for general and classical connections, Ann. Polon. Math. 99 (2010), 99-105.
- Mikulski, W. M., On prolongation of connections, Ann. Polon. Math. 97 (2) (2010), 101-121.
- Plaszczyk, M., The constructions of general connections on second jet prolongation, Ann. Univ. Mariae Curie-Skłodowska Sect. A 68 (1) (2014), 67-89.
NotesEmbed ?
topYou 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.