Some natural operators on vector fields

Jiří M. Tomáš

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 3, page 239-249
  • ISSN: 0044-8753

Abstract

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We determine all natural operators transforming vector fields on a manifold M to vector fields on T * T 1 2 M , dim M ≥ 2 , and all natural operators transforming vector fields on M to functions on T * T T 1 2 M , dim M ≥ 3 . We describe some relations between these two kinds of natural operators.

How to cite

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Tomáš, Jiří M.. "Some natural operators on vector fields." Archivum Mathematicum 031.3 (1995): 239-249. <http://eudml.org/doc/247673>.

@article{Tomáš1995,
abstract = {We determine all natural operators transforming vector fields on a manifold $M$ to vector fields on $T^*T^2_1M$, $\operatorname\{dim\}M \ge 2$, and all natural operators transforming vector fields on $M$ to functions on $T^*TT^2_1M$, $\operatorname\{dim\}M \ge 3$. We describe some relations between these two kinds of natural operators.},
author = {Tomáš, Jiří M.},
journal = {Archivum Mathematicum},
keywords = {vector field; natural bundle; natural operator; Weil bundle; natural bundle; Weil bundle; natural operators; vector fields},
language = {eng},
number = {3},
pages = {239-249},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some natural operators on vector fields},
url = {http://eudml.org/doc/247673},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Tomáš, Jiří M.
TI - Some natural operators on vector fields
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 3
SP - 239
EP - 249
AB - We determine all natural operators transforming vector fields on a manifold $M$ to vector fields on $T^*T^2_1M$, $\operatorname{dim}M \ge 2$, and all natural operators transforming vector fields on $M$ to functions on $T^*TT^2_1M$, $\operatorname{dim}M \ge 3$. We describe some relations between these two kinds of natural operators.
LA - eng
KW - vector field; natural bundle; natural operator; Weil bundle; natural bundle; Weil bundle; natural operators; vector fields
UR - http://eudml.org/doc/247673
ER -

References

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  1. The canonical isomorphism between T k T * M and T * T k M , C. R. Acad. Sci. Paris 309 (1989), 1509-1514. (1989) MR1033091
  2. Natural liftings of vector fields to tangent bundles of 1 -forms, Mathematica Bohemica 116 (1991), 319-326. (1991) MR1126453
  3. Covariant Approach to Natural Transformations of Weil Bundles, Comment. Math. Univ. Carolinae (1986). (1986) MR0874666
  4. On Cotagent Bundles of Some Natural Bundles, to appear in Rendiconti del Circolo Matematico di Palermo. MR1344006
  5. On the Natural Operators on Vector Fields, Ann. Global Anal. Geometry 6 (1988), 109-117. (1988) MR0982760
  6. Natural Operations in Differential Geometry, Springer – Verlag, 1993. (1993) MR1202431
  7. Natural Transformations of Second Tangent and Cotangent Bundles, Czechoslovak Math. (1988), 274-279. (1988) MR0946296
  8. Some results on second tangent and cotangent spaces, Quaderni dell’Università di Lecce (1978). (1978) 

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