We determine all natural transformations T²₁T*→ T*T²₁ where $T^r_k M = J^r_0 (ℝ^k,M)$. We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.
Department of Mathematics Technical University of Brno Technická 2 616 69 Brno Czechoslovakia
Bibliografia
[1] F. Cantrijn, M. Crampin, W. Sarlet and D. Saunders, The canonical isomorphism between $T^kT*M$ and $T*T^kM$, C. R. Acad. Sci. Paris 309 (1989), 1509-1514.
[2] H. Gollek, Anwendungen der Jet-Theorie auf Faserbündel und Liesche Transformationsgruppen, Math. Nachr. 53 (1972), 161-180.
[3] J. Janyška, Geometrical properties of prolongation functors, Čas. Pěst. Mat. 110 (1985), 77-86.
[4] P. Kobak, Natural liftings of vector fields to tangent bundles of 1-forms, ibid., to appear.
[5] I. Kolář and Z. Radziszewski, Natural transformations of second tangent and cotangent functors, Czechoslovak Math. J. 38 (113) (1988), 274-279.
[6] I. Kolář, P. W. Michor and J. Slovák, Natural Operations in Differential Geometry, to appear.
[7] M. Modugno and G. Stefani, Some results on second tangent and cotangent spaces, Quaderni dell'Instituto di Matematica dell'Università di Lecce, Q. 16, 1978.
[8] A. Nijenhuis, Natural bundles and their general properties, in: Differential Geometry in honor of Yano, Kinokuniya, Tokyo 1972, 317-334
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv56z1p67bwm
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