The constructions of general connections on second jet prolongation

Mariusz Plaszczyk

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.

Full Text:

PDF

References


Doupovec, M., Mikulski, W., Holonomic extension of connections and symmetrization of jets, Rep. Math. Phys. 60 (2007), 299–316.

Ehresmann, C., Sur les connexions d’ordre supérieur, Atti del V. Cong. del’Unione Mat. Italiana, 1955, Cremonese, Roma, 1956, 344–346.

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.

Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.

Kolář, I., Prolongations of generalized connections, Differential Geometry (Budapest, 1979), Colloq. Math. Soc. János Bolyai, 31, North-Holland, Amsterdam, 1982, 317-325.

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.

Kurek, J., Mikulski, W., On prolongations of projectable connections, Ann. Polon. Math. 101 (2011), no. 3, 237-250.

Mikulski, W., On “special” fibred coordinates for general and classical connections, Ann. Polon. Math. 99 (2010), 99-105.

Mikulski, W., Higher order linear connections from first order ones, Arch. Math. (Brno) 43 (2007), 285-288.




DOI: http://dx.doi.org/10.2478/umcsmath-2014-0008
Date of publication: 2015-05-23 16:29:36
Date of submission: 2015-05-04 21:50:27


Statistics


Total abstract view - 612
Downloads (from 2020-06-17) - PDF - 404

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica