Lifting of projectable vector fields to vertical fiber product preserving vector bundles

Włodzimierz M. Mikulski

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 265-271
  • ISSN: 0044-8753

Abstract

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We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.

How to cite

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Mikulski, Włodzimierz M.. "Lifting of projectable vector fields to vertical fiber product preserving vector bundles." Archivum Mathematicum 042.3 (2006): 265-271. <http://eudml.org/doc/249808>.

@article{Mikulski2006,
abstract = {We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {fibered manifolds; vector bundle functors; natural operators; natural transformations; fibered manifolds; vector bundle functors; natural operators},
language = {eng},
number = {3},
pages = {265-271},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lifting of projectable vector fields to vertical fiber product preserving vector bundles},
url = {http://eudml.org/doc/249808},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Lifting of projectable vector fields to vertical fiber product preserving vector bundles
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 265
EP - 271
AB - We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles.
LA - eng
KW - fibered manifolds; vector bundle functors; natural operators; natural transformations; fibered manifolds; vector bundle functors; natural operators
UR - http://eudml.org/doc/249808
ER -

References

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  1. Natural operators transforming vector fields to the second order tangent bundle, Časopis pěst. mat. 115 (1990), 64–72. Zbl0712.58003MR1044015
  2. On the natural operators transforming vector fields to the r -th tensor power, Suppl. Rend. Math. Circ. Palermo II(32) (1993), 15–20. MR1283617
  3. Natural operations in differential geometry, Springer-Verlag, Berlin 1993. MR1202431
  4. On the fiber product preserving bundle functors, Differential Geom. Appl. 11 (1999), 105–115.. MR1712139
  5. Lifting of linear vector fields to fiber product preserving vertical gauge bundles, Colloq. Math. 103(1) (2005), 33–40. MR2148947
  6. Some natural constructions on vector fields and higher order cotangent bundles, Monatsh. Math. 117 (1994), 107–115. Zbl0796.58002MR1266777
  7. Some natural operations on vector fields, Rend. Mat. Roma 12 (1992), 783–803. Zbl0766.58005MR1205977
  8. The natural operators lifting projectable vector fields to some fiber product preserving bundles, Ann. Polon. Math. 81.3 (2003), 261–271. Zbl1099.58003MR2044627

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