The natural operators lifting vector fields to generalized higher order tangent bundles

Włodzimierz M. Mikulski

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 3, page 207-212
  • ISSN: 0044-8753

Abstract

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For natural numbers r and n and a real number a we construct a natural vector bundle T ( r ) , a over n -manifolds such that T ( r ) , 0 is the (classical) vector tangent bundle T ( r ) of order r . For integers r ≥ 1 and n ≥ 3 and a real number a < 0 we classify all natural operators T | M n ⇝ T T ( r ) , a lifting vector fields from n -manifolds to T ( r ) , a .

How to cite

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Mikulski, Włodzimierz M.. "The natural operators lifting vector fields to generalized higher order tangent bundles." Archivum Mathematicum 036.3 (2000): 207-212. <http://eudml.org/doc/248517>.

@article{Mikulski2000,
abstract = {For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^\{(r),a\}$ over $n$-manifolds such that $T^\{(r),0\}$ is the (classical) vector tangent bundle $T^\{(r)\}$ of order $r$. For integers $r\ge 1$ and $n\ge 3$ and a real number $a<0$ we classify all natural operators $T_\{\vert M_n\}\rightsquigarrow TT^\{(r),a\}$ lifting vector fields from $n$-manifolds to $T^\{(r),a\}$.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {natural bundle; natural transformation; natural operator; natural bundle; natural transformation; natural operator},
language = {eng},
number = {3},
pages = {207-212},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The natural operators lifting vector fields to generalized higher order tangent bundles},
url = {http://eudml.org/doc/248517},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - The natural operators lifting vector fields to generalized higher order tangent bundles
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 3
SP - 207
EP - 212
AB - For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r),a}$ over $n$-manifolds such that $T^{(r),0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$. For integers $r\ge 1$ and $n\ge 3$ and a real number $a<0$ we classify all natural operators $T_{\vert M_n}\rightsquigarrow TT^{(r),a}$ lifting vector fields from $n$-manifolds to $T^{(r),a}$.
LA - eng
KW - natural bundle; natural transformation; natural operator; natural bundle; natural transformation; natural operator
UR - http://eudml.org/doc/248517
ER -

References

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  1. Natural operators transforming vector fields to the second order tangent bundle, Cas. pest. mat. 115 (1990), 64–72. Zbl0712.58003MR1044015
  2. On the natural operators transforming vector fields to the r -th tensor power, Suppl. Rendiconti Circolo Mat. Palermo, 32(II) (1993), 15–20. MR1283617
  3. Natural operations in differential geometry, Springer-Verlag, Berlin 1993. MR1202431
  4. Some natural operations on vector fields, Rendiconti Math. Roma 12(VII) (1992), 783–803. Zbl0766.58005MR1205977
  5. Natural transformations of vector fields on manifolds to vector fields on tangent bundles, Tsukuba J. Math. 12 (1988), 115–128. MR0949905

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