×

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.

MSC:

58A20 Jets in global analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.