The natural operators lifting vector fields to ( J r T * ) *

Włodzimierz M. Mikulski

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 4, page 255-260
  • ISSN: 0044-8753

Abstract

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For integers r ≥ 2 and n ≥ 2 a complete classification of all natural operators A : T | M n ⇝ T ( J r T * ) * lifting vector fields to vector fields on the natural bundle ( J r T * ) * dual to r -jet prolongation J r T * of the cotangent bundle over n -manifolds is given.

How to cite

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Mikulski, Włodzimierz M.. "The natural operators lifting vector fields to $(J^rT^*)^*$." Archivum Mathematicum 036.4 (2000): 255-260. <http://eudml.org/doc/248551>.

@article{Mikulski2000,
abstract = {For integers $r\ge 2$ and $n\ge 2$ a complete classification of all natural operators $A:T_\{\vert M_n\}\rightsquigarrow T(J^rT^*)^*$ lifting vector fields to vector fields on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {bundle functors; natural transformations; natural operators; bundle functors; natural transformations; natural operators},
language = {eng},
number = {4},
pages = {255-260},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The natural operators lifting vector fields to $(J^rT^*)^*$},
url = {http://eudml.org/doc/248551},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - The natural operators lifting vector fields to $(J^rT^*)^*$
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 4
SP - 255
EP - 260
AB - For integers $r\ge 2$ and $n\ge 2$ a complete classification of all natural operators $A:T_{\vert M_n}\rightsquigarrow T(J^rT^*)^*$ lifting vector fields to vector fields on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given.
LA - eng
KW - bundle functors; natural transformations; natural operators; bundle functors; natural transformations; natural operators
UR - http://eudml.org/doc/248551
ER -

References

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  1. Natural operations transforming vector fields to the second order tangent bundle, Čas. pěst. mat. 115(1990), 64–72. MR1044015
  2. Lifting of functions and vector fields to natural bundles, Dissert. Math. CCXII, Warszawa, 1983. MR0697471
  3. On natural operators on vector fields, Ann. Global Analysis and Geometry, 6(2) (1988), 109–117. MR0982760
  4. On the natural operators transforming vector fields to the r -th tensor power,, Suppl. Rendiconti Circolo Mat. Palermo, 32 (II) (1993), 15–20. MR1283617
  5. Natural operations in differential geometry, Springer-Verlag, Berlin 1993. MR1202431
  6. Natural liftings of vector fields to tangent bundles of bundles of 1-forms, Math. Boch. 116 (1991), 319–326. Zbl0743.53008MR1126453
  7. Some natural operations on vector fields, Rendiconti Math. Roma 12(VII) (1992), 783–803. Zbl0766.58005MR1205977
  8. Some natural constructions on vector fields and higher order cotangent bundles, Mh. Math. 117 (1994), 107–119. Zbl0796.58002MR1266777
  9. Natural operators on vector fields on the cotangent bundles of the bundles of (k,r)-velocities, Rend. Circ. Mat. Palermo 5431(II) (1998), 113–124 239–249. Zbl0929.58001MR1662732

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