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.
@article{bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_67, author = {Mariusz Plaszczyk}, title = {The constructions of general connections on second jet prolongation}, journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica}, volume = {68}, year = {2014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_67} }
Mariusz Plaszczyk. The constructions of general connections on second jet prolongation. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_67/
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.