# Natural transformations between T²₁T*M and T*T²₁M

Annales Polonici Mathematici (1991)

- Volume: 56, Issue: 1, page 67-77
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topMiroslav Doupovec. "Natural transformations between T²₁T*M and T*T²₁M." Annales Polonici Mathematici 56.1 (1991): 67-77. <http://eudml.org/doc/262525>.

@article{MiroslavDoupovec1991,

abstract = {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.},

author = {Miroslav Doupovec},

journal = {Annales Polonici Mathematici},

keywords = {higher order velocity; natural isomorphism; natural transformations; cotangent bundle},

language = {eng},

number = {1},

pages = {67-77},

title = {Natural transformations between T²₁T*M and T*T²₁M},

url = {http://eudml.org/doc/262525},

volume = {56},

year = {1991},

}

TY - JOUR

AU - Miroslav Doupovec

TI - Natural transformations between T²₁T*M and T*T²₁M

JO - Annales Polonici Mathematici

PY - 1991

VL - 56

IS - 1

SP - 67

EP - 77

AB - 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.

LA - eng

KW - higher order velocity; natural isomorphism; natural transformations; cotangent bundle

UR - http://eudml.org/doc/262525

ER -

## References

top- [1] F. Cantrijn, M. Crampin, W. Sarlet and D. Saunders, The canonical isomorphism between ${T}^{k}T*M$ and $T*{T}^{k}M$, C. R. Acad. Sci. Paris 309 (1989), 1509-1514. Zbl0702.58006
- [2] H. Gollek, Anwendungen der Jet-Theorie auf Faserbündel und Liesche Transformationsgruppen, Math. Nachr. 53 (1972), 161-180. Zbl0245.58002
- [3] J. Janyška, Geometrical properties of prolongation functors, Čas. Pěst. Mat. 110 (1985), 77-86. Zbl0582.58002
- [4] P. Kobak, Natural liftings of vector fields to tangent bundles of 1-forms, ibid., to appear. Zbl0743.53008
- [5] I. Kolář and Z. Radziszewski, Natural transformations of second tangent and cotangent functors, Czechoslovak Math. J. 38 (113) (1988), 274-279. Zbl0669.53023
- [6] I. Kolář, P. W. Michor and J. Slovák, Natural Operations in Differential Geometry, to appear. Zbl0782.53013
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.