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Keywords:
tangent bundle; jet bundle; connection; natural operator.
tangent bundle; jet bundle; connection; natural operator.
Summary:
All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
References:
[1] D. Canarutto A. Jadczyk M. Modugno: Quantum mechanics of a spin particle in a curved spacetime with absolute time. Rep. on Math. Phys., 36, 1 (1995), 95–140. MR 1377229
[2] A. Jadczyk M. Modugno: An outline of a new geometric approach to Galilei general relativistic quantum mechanics. in C.N. Yang, M.L. Ge and X. W. Zhou editors, Proc. XXI Int. Conf. on Differential geometric methods in theoretical physics, Tianjin 5-9 June 1992, 543-556, Singapore, 1992, World Scientific.
[3] A. Jadczyk M. Modugno: Galilei general relativistic quantum mechanics. book manuscript, 1994.
[4] I. Kolář P. W. Michor J. Slovák: Natural Operations in Differential Geometry. Springer–Verlag, 1993. MR 1202431
[5] D. Krupka J. Janyška: Lectures on Differential Invariants. Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990. MR 1108622
[6] L. Mangiarotti M. Modugno: Connections and differential calculus on fibred manifolds. Istituto di Matematica Applicata “G. Sansone”, Università di Firenze, 1989.
[7] A. Nijenhuis: Natural bundles and their general properties. Diff. Geom., in honour of K. Yano, Kinokuniya, Tokyo 1972, pp. 317–334. MR 0380862 | Zbl 0246.53018
[8] J. Slovák: On the finite order of some operators. Proc. Conf. Diff. Geom. and Its Appl. (communications), Brno 1986, Published by J. E. Purkyně University 1987, 283-294. MR 0923390
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