Natural transformations of higher order cotangent bundle functors

Jan Kurek

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 1, page 29-35
  • ISSN: 0066-2216

Abstract

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We determine all natural transformations of the rth order cotangent bundle functor T r * into T s * in the following cases: r = s, r < s, r > s. We deduce that all natural transformations of T r * into itself form an r-parameter family linearly generated by the pth power transformations with p =1,...,r.

How to cite

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Jan Kurek. "Natural transformations of higher order cotangent bundle functors." Annales Polonici Mathematici 58.1 (1993): 29-35. <http://eudml.org/doc/262276>.

@article{JanKurek1993,
abstract = {We determine all natural transformations of the rth order cotangent bundle functor $T^\{r*\}$ into $T^\{s*\}$ in the following cases: r = s, r < s, r > s. We deduce that all natural transformations of $T^\{r*\}$ into itself form an r-parameter family linearly generated by the pth power transformations with p =1,...,r.},
author = {Jan Kurek},
journal = {Annales Polonici Mathematici},
keywords = {higher order cotangent bundle; jet; pth power transformation; jets; -th power transformation},
language = {eng},
number = {1},
pages = {29-35},
title = {Natural transformations of higher order cotangent bundle functors},
url = {http://eudml.org/doc/262276},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Jan Kurek
TI - Natural transformations of higher order cotangent bundle functors
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 1
SP - 29
EP - 35
AB - We determine all natural transformations of the rth order cotangent bundle functor $T^{r*}$ into $T^{s*}$ in the following cases: r = s, r < s, r > s. We deduce that all natural transformations of $T^{r*}$ into itself form an r-parameter family linearly generated by the pth power transformations with p =1,...,r.
LA - eng
KW - higher order cotangent bundle; jet; pth power transformation; jets; -th power transformation
UR - http://eudml.org/doc/262276
ER -

References

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  1. [1] J. Gancarzewicz, Differential Geometry, PWN, Warszawa 1987 (in Polish). 
  2. [2] I. Kolář, Some natural operators in differential geometry, in: Proc. Conf. Diff. Geom. and its Applications, Brno 1986, Kluwer, Dordrecht 1987, 91-110. 
  3. [3] I. Kolář and G. Vosmanska, Natural transformations of higher order tangent bundles and jet spaces, Časopis Pěst. Mat. 114 (2) (1989), 181-186. Zbl0678.58002
  4. [4] I. Kolář, P. Michor and J. Slovak, Natural Operations in Differential Geometry, to appear. Zbl0782.53013
  5. [5] J. Kurek, On natural operators on sectorform fields, Časopis Pěst. Mat. 115 (3) (1990), 232-239. Zbl0706.58003

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