On the existence of prolongation of connections

Miroslav Doupovec; Włodzimierz M. Mikulski

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 4, page 1323-1334
  • ISSN: 0011-4642

Abstract

top
We classify all bundle functors G admitting natural operators transforming connections on a fibered manifold Y → M into connections on G Y → M . Then we solve a similar problem for natural operators transforming connections on Y → M into connections on G Y → Y .

How to cite

top

Doupovec, Miroslav, and Mikulski, Włodzimierz M.. "On the existence of prolongation of connections." Czechoslovak Mathematical Journal 56.4 (2006): 1323-1334. <http://eudml.org/doc/31107>.

@article{Doupovec2006,
abstract = {We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y\rightarrow M$ into connections on $GY\rightarrow M$. Then we solve a similar problem for natural operators transforming connections on $Y\rightarrow M$ into connections on $GY\rightarrow Y$.},
author = {Doupovec, Miroslav, Mikulski, Włodzimierz M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {bundle functor; connection; natural operator; bundle functor; connection; natural operator},
language = {eng},
number = {4},
pages = {1323-1334},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of prolongation of connections},
url = {http://eudml.org/doc/31107},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Doupovec, Miroslav
AU - Mikulski, Włodzimierz M.
TI - On the existence of prolongation of connections
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1323
EP - 1334
AB - We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y\rightarrow M$ into connections on $GY\rightarrow M$. Then we solve a similar problem for natural operators transforming connections on $Y\rightarrow M$ into connections on $GY\rightarrow Y$.
LA - eng
KW - bundle functor; connection; natural operator; bundle functor; connection; natural operator
UR - http://eudml.org/doc/31107
ER -

References

top
  1. On natural operators transforming connections to the tangent bundle of a fibred manifold, Knižnice VUT Brno B-119 (1988), 47–56. (1988) 
  2. 10.1007/s006050170010, Monatshefte Math. 134 (2001), 39–50. (2001) MR1872045DOI10.1007/s006050170010
  3. Prolongation of pairs of connections into connections on vertical bundles, Arch. Math. (Brno) 41 (2005), 409–422. (2005) MR2195494
  4. Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibered manifold, Arch. Math. (Brno) 32 (1996), 281–288. (1996) MR1441399
  5. Some natural operations with connections, Jour. Nat. Math. India 5 (1987), 127–141. (1987) MR0994555
  6. Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
  7. Natural lifting of connections to vertical bundles, Rend. Circ. Mat. Palermo, Serie II, Suppl. 63 (2000), 97–102. (2000) MR1758084
  8. Non-existence of some canonical constructions on connections, Comment Math. Univ. Carolinae 44.4 (2003), 691–695. (2003) Zbl1099.58004MR2062885
  9. Non-existence of natural operators transforming connections on Y → M into connections on F Y → Y , Arch. Math. (Brno) 41 (2005), 1–4. (2005) MR2142138
  10. Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Math. 15.3 (2000), 421–512. (2000) Zbl0992.34006MR1825970

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.