Natural relations between connections in 2-fibred manifolds
In the paper, a new approach to the study of interrelations between connections within the framework of a general 2-fibred manifold is introduced. The role of a naturality of the constructions is discussed and the formalism is applied in two particular situations. First, natural relations between connections in J 1 Y→ Y → X are studied and their role for the integrability of partial differential equations represented by connections in question is described. Secondly, the 2-fibred manifold VY → Y → X is investigated. In this case, the importance for a description of the symmetries of equations under consideration is pointed out.
KeywordsVector Bundle Natural Transformation Natural Relation Linear Connection Natural Operation
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- 1.M. Crampin, E. Martínez, and W. Sarlet: Linear connections for systems of second-order ordinary differential equations, preprint, 1994Google Scholar
- 2.M. Doupovec and A. Vondra: On certain natural transformations between connections, in: Proc. Conf. Diff. Geom. and Its Appl., Opava, 1992, Silesian University, Opava, 1993, 273–279.Google Scholar
- 3.M. Doupovec and A. Vondra: Some natural operations between connections on fibered manifolds, preprint, Brno, 1993Google Scholar
- 6.I. Kolář, P. W. Michor, and J. Slovák: Natural Operations in Differential Geometry, Springer, 1993Google Scholar
- 7.D. Krupka and J. Janyška: Lectures on differential invariants, Folia Fac. Sci. Nat. Univ. Purk. Brun. Phys., J. E. Purkyne University, 1990, BrnoGoogle Scholar
- 8.O. Krupková and A. Vondra: On some integration methods for connections on fibered manifolds, in:Proc. Conf. Diff. Geom. and Its Appl., Opava, 1992, Silesian University, Opava, 1993, 89–101.Google Scholar
- 9.E. Martínez and J. F. Cariñena: Linear connection induced by an Ehresmann connection on the tangent bundle. Linearization of second-order differential equations, preprint, 1993Google Scholar
- 12.A. Vondra: Geometry of second-order connections and ordinary differential equations, preprint, Brno, 1993Google Scholar