# Some natural operators on vector fields

Archivum Mathematicum (1995)

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

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topTomáš, 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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- On Cotagent Bundles of Some Natural Bundles, to appear in Rendiconti del Circolo Matematico di Palermo. MR1344006
- On the Natural Operators on Vector Fields, Ann. Global Anal. Geometry 6 (1988), 109-117. (1988) MR0982760
- Natural Operations in Differential Geometry, Springer – Verlag, 1993. (1993) MR1202431
- Natural Transformations of Second Tangent and Cotangent Bundles, Czechoslovak Math. (1988), 274-279. (1988) MR0946296
- Some results on second tangent and cotangent spaces, Quaderni dell’Università di Lecce (1978). (1978)

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