Higher order jet prolongations type gauge natural bundles over vector bundles
Abstract
Let r ≥ 3 and m ≥ 2 be natural numbers and E be a vector bundle with m-dimensional basis. We find all gauge natural bundles similar to the r-jet prolongation bundle J^r E of E. We also find all gauge natural bundles similar to the vector r-tangent bundle (J^r_fl(E,R)_0)* of E.
References
J. Aczél, S. Go l ,ab, Funktionalgleichungen der Theorie der geometrischen Objekte, Monografie Matematyczne, Warszawa, PWN, 1960.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. D ,ebecki, J. Gancarzewicz, M. de Leon, W.M. Mikulski, Invariants of Lagrangians and their classifications, J. Math. Phys. 35(9) (1994), 4568-4593.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Doupovec, Natural operators transforming vector fields to the second order tangent bundle, Časopis Pěst. Mat. 115 (1990), 64-72.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Doupovec, I. Kolář, On the jets of fibered manifold morphisms, Cahiers Topologie Géom. Différentielle Catég. 40 (1999), 21-30.
##plugins.generic.googleScholarLinks.settings.viewInGS##
D.J. Eck, Product-precerving functors on smooth manifolds, J. Pure Appl. Algebra 42 (1986), 133-140.
##plugins.generic.googleScholarLinks.settings.viewInGS##
D.J. Eck, Gauge natural bundles and generalized gauge theories, Mem. Amer. Math. Soc. 33 (1981), no. 247.
##plugins.generic.googleScholarLinks.settings.viewInGS##
D.B.A. Epstein, W.P. Thurston, Transformation groups and natural bundles, Proc. London Math. Soc. (3)38 (1979), 219-236.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Gancarzewicz, Liftings of functions and vector fields to natural bundles, Dissertationes Math. 212 (1983).
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Gancarzewicz, I. Kolář, Some gauge-natural operators on linear connections, Monatsh. Math. 111 (1991), 23-33.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Gancarzewicz, W. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to a product preserving functor, Nagoya Math. J. 135 (1994), 1-41.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Janyška, D. Krupka, Lectures on differential invariants, Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis. Mathematica, 1., 1990.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Kainz, P. Michor, Natural transformations in differential geometry, Czechoslovak Math. J. 37(112) (1987), 584-607.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář, On natural operators on vector fields, Ann. Global Anal. Geom. 6(2) (1988), 109-117.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář, Gauge-natural forms of Chern-Weil type, Ann. Global Anal. Geom. 11 (1993), 41-47.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář, Natural operators related with the variational calculus, Differential Geom. and Its Appl. Proceedings Opava (1993), 461-472.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář, Bundle functors of jet type, Differential Geom. and Appl. Proc. of the 7th International Conference Brno (1998), 231-237.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář, P.W. Michor, J. Slovák, Natural Operations in Differential Geometry, Springer Verlag, Berlin, 1993.
##plugins.generic.googleScholarLinks.settings.viewInGS##
I. Kolář , W.M. Mikulski, On the fiber product preserving bundle functors, . Differential Geom. Appl. 11 (1999), 105-115.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Kurek, On the natural operators of Bianchi type, Arch. Math. (Brno) 27a (1991), 25-29.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Kurek, W.M. Mikulski, The natural operators lifting 1-forms to some vector bundle functors, Colloq. Math. 93(2) (2002), 259-265.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Kureš, W.M. Mikulski, Natural operators lifting vector fields to bundles of Weil contact elements, Czechoslovak Math. J. 54(129) (2004), no. 4, 855-867.
##plugins.generic.googleScholarLinks.settings.viewInGS##
K. Lubaś, A. Zajtz, Estimates of the action order of some jet groups, Proc. Conf. Differential Geometry and Appl. Brno (1998), Masaryk University in Brno (1999), 247-257.
##plugins.generic.googleScholarLinks.settings.viewInGS##
O.O. Luciano, Categories of multiplicative functors and Morimoto’s conjecture, Preprint 46, Inst. Fourier, Laboratoire des Mathématiques, Grenoble, 1986.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, There exists a prolongation functor of infinite order, Časopis Pěst. Mat. 114 (1989), 57-59.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, Product preserving bundle functors on fibered manifolds, Arch. Math. (Brno) 32(4) (1996), 307-316.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, On the product preserving bundle functors on k-fibered manifolds, Demonstratio Math. 34(3) (2001), 693-700.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, Product preserving gauge bundle functors on vector bundles, Colloq. Math. 90(2) (2001), 277-285.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, On the fiber product preserving gauge bundle functors on vector bundles, Ann. Polon. Math. 82 (2003), no. 3, 251-264.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, The natural affinors on the r-jet prolongations of a vector bundle, Demonstratio Math. 37 (2004), no. 3, 709-717.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W.M. Mikulski, J. Tomáš, Product preserving bundle functors on fibered manifolds, Colloq. Math. 96 (2003), no. 1, 17-26.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Nijenhuis, Natural bundles and their general properties, Geometric objects revisited. Differential geometry (in honor of Kentaro Yano), pp. 317-334. Kinokuniya, Tokyo, 1972.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R.S. Palais, C.-L. Terng, Natural bundles have finite order, Topology 16 (1977), 271-277.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Paluszny, A. Zajtz, Foundation of the geometry of natural bundles, Lect. Notes Univ. Caracas, 1984.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Slovák, Peetre theorem for nonlinear operators, Ann. Global Anal. Geom. 6 (1988), 273-283.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Zajtz, Geometric object with finitely determined germs, Ann. Polon. Math. 49 (1988), 157-168.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Zajtz, On the order of natural differential operators and liftings, Ann. Polon. Math. 49 (1988), 169-178.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Zajtz, A classification of natural bundles, Colloq. Math. Soc. János Bolyai,, 46, Topics in differential geometry, Vol. I, II (Debrecen, 1984), 1333-1357.
##plugins.generic.googleScholarLinks.settings.viewInGS##
A. Zajtz, The sharp upper bound on the order of natural bundles of given dimension, Bull. Soc. Math. Belg. Sér. B 39 (1987), 347-357.
##plugins.generic.googleScholarLinks.settings.viewInGS##
