Previous |  Up |  Next


bundle functor; Weil bundle; natural transformation
For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with $m$-dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.
[1] M. Doupovec and I.  Kolář: Iteration of fiber product preserving bundle functors. Monatsh. Math. 134 (2001), 39–50. DOI 10.1007/s006050170010 | MR 1872045
[2] I. Kolář: Affine structure on Weil bundles. Nagoya Math.  J. 158 (2000), 99–106. MR 1766571
[3] I. Kolář: A general point of view to nonholonomic jet bundles. Cahiers Topo. Geom. Diff. Categoriques XLIV (2003), 149–160. MR 1985835
[4] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry. Springer-Verlag, 1993. MR 1202431
[5] I. Kolář and W. M. Mikulski: On the fiber product preserving bundle functors. Diff. Geom. Appl. 11 (1999), 105–115. DOI 10.1016/S0926-2245(99)00022-4 | MR 1712139
[6] M. Kureš: On the simplicial structure of some Weil bundles. Rend. Circ. Mat. Palermo, Serie  II, Suppl. 63 (2000), 131–140. MR 1758088
[7] J. E. White: The Method of Iterated Tangents with Applications in Local Riemannian Geometry. Pitman Press, , 1982. MR 0693620 | Zbl 0478.58002
Partner of
EuDML logo