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jet of fibered manifold morphism; contact element; Weil bundle; natural operator
For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
[1] R. Alonso: Jet manifold associated to a Weil bundle. Arch. Math. (Brno) 36 (2000), 195–199. MR 1785036 | Zbl 1049.58007
[2] A. Cabras and I. Kolář: Prolongation of projectable tangent valued forms. To appear in Rendiconti Palermo. MR 1942654
[3] M. Doupovec and I. Kolář: On the jets of fibered manifold morphisms. Cahiers Topo. Géom. Diff. Catégoriques XL (1999), 21–30. MR 1682575
[4] C. Ehresmann: Oeuvres complètes et commentées. Parties I-A et I-2. Cahiers Topo. Géom. Diff. XXIV (1983).
[5] I. Kolář: Affine structure on Weil bundles. Nagoya Math. J. 158 (2000), 99–106. MR 1766571
[6] I. Kolář: Covariant approach to natural transformations of Weil functors. Comment. Math. Univ. Carolin. 27 (1986), 723–729. MR 0874666
[7] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry. Springer-Verlag, 1993. MR 1202431
[8] I. Kolář and W. M. Mikulski: Natural lifting of connections to vertical bundles. Supplemento ai Rendiconti del Circolo Mat. di Palermo, Serie II 63 (2000), 97–102. MR 1758084
[9] W. M. Mikulski: The Natural operators lifting 1-forms on manifolds to the bundles of $A$-velocities. Mh. Math. 119 (1995), 63–77. DOI 10.1007/BF01292769 | MR 1315684 | Zbl 0823.58004
[10] W. M. Mikulski: Product preserving bundle functors on fibered manifolds. Arch. Math. (Brno) 32 (1996), 307–316. MR 1441401 | Zbl 0881.58002
[11] J. Muñoz, F. J. Muriel and J. Rodríguez: Weil bundles and jet spaces. Czechoslovak Math. J. 50 (2000), 721–748. DOI 10.1023/A:1022408527395 | MR 1792967
[12] J. Tomáš: Natural operators transforming projectable vector fields to products preserving bundles. Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 59 (1999), 181–187. MR 1692269
[13] A. Weil: Théorie des points proches sur les variétés différentielles. Collogue de C.N.R.S, Strasbourg, 1953, pp. 111–117. MR 0061455
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