Natural transformations of separated jets

Miroslav Doupovec; Ivan Kolář

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 4, page 297-303
  • ISSN: 0044-8753

Abstract

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Given a map of a product of two manifolds into a third one, one can define its jets of separated orders r and s . We study the functor J of separated ( r ; s ) -jets. We determine all natural transformations of J into itself and we characterize the canonical exchange J → J s ; r from the naturality point of view.

How to cite

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Doupovec, Miroslav, and Kolář, Ivan. "Natural transformations of separated jets." Archivum Mathematicum 036.4 (2000): 297-303. <http://eudml.org/doc/248537>.

@article{Doupovec2000,
abstract = {Given a map of a product of two manifolds into a third one, one can define its jets of separated orders $r$ and $s$. We study the functor $J$ of separated $(r;s)$-jets. We determine all natural transformations of $J$ into itself and we characterize the canonical exchange $J\rightarrow J^\{s;r\}$ from the naturality point of view.},
author = {Doupovec, Miroslav, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {separated jet; canonical exchange; natural transformation; separated jet; canonical exchange; natural transformation},
language = {eng},
number = {4},
pages = {297-303},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Natural transformations of separated jets},
url = {http://eudml.org/doc/248537},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Doupovec, Miroslav
AU - Kolář, Ivan
TI - Natural transformations of separated jets
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 4
SP - 297
EP - 303
AB - Given a map of a product of two manifolds into a third one, one can define its jets of separated orders $r$ and $s$. We study the functor $J$ of separated $(r;s)$-jets. We determine all natural transformations of $J$ into itself and we characterize the canonical exchange $J\rightarrow J^{s;r}$ from the naturality point of view.
LA - eng
KW - separated jet; canonical exchange; natural transformation; separated jet; canonical exchange; natural transformation
UR - http://eudml.org/doc/248537
ER -

References

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  1. Jets infinitésimaux d’ordre séparé supérieur, Proc. Japan Acad. 37 (1961), 18–22. Zbl0840.58004MR0160167
  2. On some operations with connections, Math. Nachr. 69 (1975), 297–306. MR0391157
  3. Natural Operations in Differential Geometry, Springer-Verlag, 1993. MR1202431
  4. Natural transformations of higher order tangent bundles and jet spaces, Čas. pěst. mat. 114 (1989), 181–186. MR1063764
  5. Introduction to the theory of semi-holonomic jets, Archivum Math. (Brno) 33 (1997), 173–189. Zbl0915.58004MR1478771

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