The tangent bundle of higher order. (English) Zbl 0955.58001

Introduction: There are various definitions of tangent bundle such as algebraic, geometric, and physical ones [see for example Th. Bröcker and K. Jänich, “Introduction to differential topology”, Cambridge University Press (1982; Zbl 0486.57001)]. The concept of the tangent bundle of higher order is due to W. F. Newns and A. G. Walker [J. Lond. Math. Soc. 31, 400-406 (1956; Zbl 0071.15303)].
In this paper, we give two new definitions of tangent bundle of higher order over a finite dimensional Hausdorff manifold, and we show that they are equivalent.


58A20 Jets in global analysis
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[1] Bröcker, T. H.; Jänich, K., Introduction to differentiable topology (1973), Cambridge Univ. Press: Cambridge Univ. Press New York
[2] Ehresmann, C., Les prolongements d’une variete differentiable: I. Calcul des jets, II. L’espace des jets d’order r de \(V_n\) dan \(V_m\), III. Transitive des prolongations, C.R. Acad. Sci. Paris, 233, 1081-1083 (1956) · Zbl 0043.17401
[3] Gamkerlidze, R. V., Geometry I: Basic ideas and concepts of differential geometry, (EMS, 28 (1991), Springer Verlag: Springer Verlag New York) · Zbl 0741.00027
[4] Molino, P., Theorie des G-structures: Le problem d’equivalance, (LNM, 588 (1977), Springer Verlag: Springer Verlag New York) · Zbl 0357.53022
[5] Newns, N.; Walker, A., Tangent planes to a differentiable manifolds, J. London Math Soc., 31, 400-407 (1956), London · Zbl 0071.15303
[6] Reinhart, B. L., Differential geometry of foliations (1983), Springer Verlag: Springer Verlag Berlin · Zbl 0506.53018
[7] Shafarevich, I. R., (Basic Algebraic geometry, 2 vols. (1994), Springer Verlag: Springer Verlag Berlin) · Zbl 0797.14002
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