Canonical 1-forms on higher order adapted frame bundles

Jan Kurek; Włodzimierz M. Mikulski

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 2, page 115-118
  • ISSN: 0044-8753

Abstract

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Let ( M , ) be a foliated m + n -dimensional manifold M with n -dimensional foliation . Let V be a finite dimensional vector space over 𝐑 . We describe all canonical ( ol m , n -invariant) V -valued 1 -forms Θ : T P r ( M , ) V on the r -th order adapted frame bundle P r ( M , ) of ( M , ) .

How to cite

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Kurek, Jan, and Mikulski, Włodzimierz M.. "Canonical 1-forms on higher order adapted frame bundles." Archivum Mathematicum 044.2 (2008): 115-118. <http://eudml.org/doc/250286>.

@article{Kurek2008,
abstract = {Let $(M,\mathcal \{F\})$ be a foliated $m+n$-dimensional manifold $M$ with $n$-dimensional foliation $\mathcal \{F\}$. Let $V$ be a finite dimensional vector space over $\mathbf \{R\}$. We describe all canonical ($\{\mathcal \{F\}\}\mbox\{\it ol\}_\{m,n\}$-invariant) $V$-valued $1$-forms $\Theta \colon TP^r(M,\{\mathcal \{F\}\}) \rightarrow V$ on the $r$-th order adapted frame bundle $P^r(M,\mathcal \{F\})$ of $(M,\mathcal \{F\})$.},
author = {Kurek, Jan, Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {foliated manifold; infinitesimal automorphism; higher order adapted frame bundle; canonical $1$-form; foliated manifold; infinitesimal automorphism; higher order adapted frame bundle, canonical 1-form},
language = {eng},
number = {2},
pages = {115-118},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Canonical 1-forms on higher order adapted frame bundles},
url = {http://eudml.org/doc/250286},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Kurek, Jan
AU - Mikulski, Włodzimierz M.
TI - Canonical 1-forms on higher order adapted frame bundles
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 2
SP - 115
EP - 118
AB - Let $(M,\mathcal {F})$ be a foliated $m+n$-dimensional manifold $M$ with $n$-dimensional foliation $\mathcal {F}$. Let $V$ be a finite dimensional vector space over $\mathbf {R}$. We describe all canonical (${\mathcal {F}}\mbox{\it ol}_{m,n}$-invariant) $V$-valued $1$-forms $\Theta \colon TP^r(M,{\mathcal {F}}) \rightarrow V$ on the $r$-th order adapted frame bundle $P^r(M,\mathcal {F})$ of $(M,\mathcal {F})$.
LA - eng
KW - foliated manifold; infinitesimal automorphism; higher order adapted frame bundle; canonical $1$-form; foliated manifold; infinitesimal automorphism; higher order adapted frame bundle, canonical 1-form
UR - http://eudml.org/doc/250286
ER -

References

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  1. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer Verlag, 1993. (1993) MR1202431
  2. Wolak, R. A., Geometric structures on foliated manifolds, Publications del Departamento de Geometria y Topologia, Universidad de Santiago de Compostella 76 (1989). (1989) Zbl0838.53029MR1040852

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