Geodesic
Invariant subspaces in higher order jet prolongations of a fibred manifold
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 209-220 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used.
We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used.
Classification : 53A55, 53C05, 58A20
Keywords: 2-fibred manifold; jet prolongation; semiholonomic jets; natural transformation; connection 
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Doupovec, Miroslav; Vondra, Alexandr. Invariant subspaces in higher order jet prolongations of a fibred manifold. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 209-220. http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a21/

[1] M. Doupovec and A. Vondra: On certain natural transformations between connections. Proc. Conf. Diff. Geom. and Its Appl., Opava, 1992, Silesian University, Opava, 1993, pp. 273–279. | MR

[2] M. Doupovec and A. Vondra: Some natural operations between connections on fibered manifolds. Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 39 (1996), 73–84. | MR

[3] M. Doupovec and A. Vondra: Natural relations between connections in $2$-fibred manifolds. New Developments in Differential Geometry, Proceedings, Kluwer Academic Publishers, Dordrecht, 1996, pp. 113–130. | MR

[4] I. Kolář: Connections in 2-fibred manifolds. Arch. Math. (Brno) 17 (1981), 23–30.

[5] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry. Springer Verlag, 1993. | MR

[6] D. Krupka and J. Janyška: Lectures on differential invariants. Folia Fac. Sci. Natur. Univ. Purk. Brun. Phys., Brno, 1990. | MR

[7] L. Mangiarotti and M. Modugno: Fibred spaces, jet spaces and connections for field theories. Proceedings of International Meeting “Geometry and Physics”, Florence, 1982, Pitagora Editrice, Bologna, 1983, pp. 135–165. | MR

[8] L. Mangiarotti and M. Modugno: Connections and differential calculus on fibred manifolds. Aplications to field theory. Istituto di Matematica Applicata “G. Sansone", Firense, 1989, 1–147.

[9] D. J. Saunders: The Geometry of Jet Bundles. London Mathematical Society Lecture Note Series 142, Cambridge University Press, Cambridge, 1989. | MR | Zbl

[10] A. Vondra: Towards a geometry of higher-order partial differential equations represented by connections on fibered manifolds. Brno, 1995, 1–114.