The constructions of general connections on the fibred product of q copies of the first jet prolongation

Mariusz Plaszczyk

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 \(J^{<q>}Y \rightarrow M\) of \(q\) copies of the first jet prolongation \(J^{1}Y \rightarrow M\).


Keywords


General connection; classical linear connection; first jet prolongation; bundle functor; natural operator

Full Text:

PDF

References


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.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.77-90
Date of publication: 2018-06-25 09:04:06
Date of submission: 2018-06-24 22:44:32


Statistics


Total abstract view - 1029
Downloads (from 2020-06-17) - PDF - 549

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Mariusz Plaszczyk