Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec; Włodzimierz M. Mikulski

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 4, page 409-422
  • ISSN: 0044-8753

Abstract

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Let F be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the F -vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to F -vertical bundles. We also present some examples and applications.

How to cite

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Doupovec, Miroslav, and Mikulski, Włodzimierz M.. "Prolongation of pairs of connections into connections on vertical bundles." Archivum Mathematicum 041.4 (2005): 409-422. <http://eudml.org/doc/249485>.

@article{Doupovec2005,
abstract = {Let $F$ be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the $F$-vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications.},
author = {Doupovec, Miroslav, Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {connection; vertical bundle; connection; vertical bundle},
language = {eng},
number = {4},
pages = {409-422},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Prolongation of pairs of connections into connections on vertical bundles},
url = {http://eudml.org/doc/249485},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Doupovec, Miroslav
AU - Mikulski, Włodzimierz M.
TI - Prolongation of pairs of connections into connections on vertical bundles
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 4
SP - 409
EP - 422
AB - Let $F$ be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the $F$-vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications.
LA - eng
KW - connection; vertical bundle; connection; vertical bundle
UR - http://eudml.org/doc/249485
ER -

References

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  1. Prolongation of second order connections to vertical Weil bundles, Arch. Math. (Brno) 37 (2001), 333–347. MR1879456
  2. On the natural operators transforming connections to the tangent bundle of a fibred manifold, Knižnice VUT Brno, B-119 (1988), 47–56. 
  3. Liftings of functions and vector fields to natural bundles, Dissertationes Math. Warszawa 1983. Zbl0517.53016MR0697471
  4. Natural liftings of vector fields to tangent bundles of bundles of 1 -forms, Math. Bohem. 3 (116) (1991), 319–326. Zbl0743.53008MR1126453
  5. Some natural operations with connections, J. Nat. Acad. Math. India 5 (1987), 127–141. MR0994555
  6. Prolongations of vector fields to jet bundles, Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 103–111. MR1061792
  7. Natural Operations in Differential Geometry, Springer-Verlag 1993. MR1202431
  8. On the fiber product preserving bundle functors, Differential Geom. Appl. 11 (1999), 105–115. MR1712139
  9. Natural lifting of connections to vertical bundles, Rend. Circ. Mat. Palermo (2) Suppl. 63 (2000), 97–102. MR1758084
  10. Some natural operations on vector fields, Rend. Mat. Appl. (7) 12 (1992), 783–803. Zbl0766.58005MR1205977
  11. Some natural constructions on vector fields and higher order cotangent bundles, Monatsh. Math. 117 (1994), 107–119. Zbl0796.58002MR1266777
  12. The natural operators lifting vector fields to generalized higher order tangent bundles, Arch. Math. (Brno) 36 (2000), 207–212. Zbl1049.58010MR1785038
  13. Non-existence of some canonical constructions on connections, Comment. Math. Univ. Carolin. 44, 4 (2003), 691–695. Zbl1099.58004MR2062885
  14. Natural operators on vector fields on the cotangent bundles of the bundles of ( k , r ) -velocities, Rend. Circ. Mat. Palermo (2) Suppl. 54 (1988), 113–124. Zbl0929.58001MR1662732
  15. Natural T -functions on the cotangent bundle of a Weil bundle, to appear in Czechoslovak Math. J. MR2100000

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