Natural transformations between T²₁T*M and T*T²₁M

Miroslav Doupovec

Annales Polonici Mathematici (1991)

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

Abstract

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We determine all natural transformations T²₁T*→ T*T²₁ where T k r M = J 0 r ( ℝ k , M ) . We also give a geometric characterization of the canonical isomorphism ψ₂ defined by Cantrijn et al.

How to cite

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Miroslav 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

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  1. [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. [2] H. Gollek, Anwendungen der Jet-Theorie auf Faserbündel und Liesche Transformationsgruppen, Math. Nachr. 53 (1972), 161-180. Zbl0245.58002
  3. [3] J. Janyška, Geometrical properties of prolongation functors, Čas. Pěst. Mat. 110 (1985), 77-86. Zbl0582.58002
  4. [4] P. Kobak, Natural liftings of vector fields to tangent bundles of 1-forms, ibid., to appear. Zbl0743.53008
  5. [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. [6] I. Kolář, P. W. Michor and J. Slovák, Natural Operations in Differential Geometry, to appear. Zbl0782.53013
  7. [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. [8] A. Nijenhuis, Natural bundles and their general properties, in: Differential Geometry in honor of Yano, Kinokuniya, Tokyo 1972, 317-334 

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