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

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

How to cite

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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

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  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
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  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 into connections on , 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

Citations in EuDML Documents

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  1. Anna Bednarska, The vertical prolongation of the projectable connections
  2. Anna Bednarska, The vertical prolongation of the projectable connections
  3. Jacek Dębecki, Linear liftings of skew symmetric tensor fields of type to Weil bundles
  4. Włodzimierz M. Mikulski, A construction of a connection on from a connection on by means of classical linear connections on and

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