Liftings of 1 -forms to the linear r -tangent bundle

Włodzimierz M. Mikulski

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 2, page 97-111
  • ISSN: 0044-8753

Abstract

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Let r , n be fixed natural numbers. We prove that for n -manifolds the set of all linear natural operators T * → T * T ( r ) is a finitely dimensional vector space over R . We construct explicitly the bases of the vector spaces. As a corollary we find all linear natural operators T * → T r * .

How to cite

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Mikulski, Włodzimierz M.. "Liftings of $1$-forms to the linear $r$-tangent bundle." Archivum Mathematicum 031.2 (1995): 97-111. <http://eudml.org/doc/247671>.

@article{Mikulski1995,
abstract = {Let $r,n$ be fixed natural numbers. We prove that for $n$-manifolds the set of all linear natural operators $T^*\rightarrow T^*T^\{(r)\}$ is a finitely dimensional vector space over $R$. We construct explicitly the bases of the vector spaces. As a corollary we find all linear natural operators $T^*\rightarrow T^\{r*\}$.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {linear r-tangent bundle; linear natural operator; 1-form; linear -tangent bundle; linear natural operator; 1-form},
language = {eng},
number = {2},
pages = {97-111},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Liftings of $1$-forms to the linear $r$-tangent bundle},
url = {http://eudml.org/doc/247671},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Liftings of $1$-forms to the linear $r$-tangent bundle
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 2
SP - 97
EP - 111
AB - Let $r,n$ be fixed natural numbers. We prove that for $n$-manifolds the set of all linear natural operators $T^*\rightarrow T^*T^{(r)}$ is a finitely dimensional vector space over $R$. We construct explicitly the bases of the vector spaces. As a corollary we find all linear natural operators $T^*\rightarrow T^{r*}$.
LA - eng
KW - linear r-tangent bundle; linear natural operator; 1-form; linear -tangent bundle; linear natural operator; 1-form
UR - http://eudml.org/doc/247671
ER -

References

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  1. Liftings of covariant ( 0 , 2 ) -tensor fields to the bundle of k -dimensional 1 -velocities, Suppl. Rend. Circ. Mat. Palermo (in press). 
  2. Liftings of 1-forms to the tangent bundle of higher order, Czech. Math. J. 40 (115) (1990), 397–407. MR1065019
  3. Natural operations with projectable tangent valued forms on fibered manifolds, Annali di Math. CLIX (1991), 171–184. 
  4. Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. MR1202431
  5. On the first order natural operators transforming 1-forms on a manifold to linear frame bundle, Demonstratio Math. 26 (1993), 287–293. MR1240218
  6. On the first order natural operators transforming 1-forms on a manifold to the tangent bundle, Ann. U.M.C.S. 43 (1989), 79–83. Zbl0739.58001MR1158100
  7. The natural operators lifting 1-forms on manifolds to the bundles of A -velocities, Mh. Math., 119 (1995), 63–77. Zbl0823.58004MR1315684
  8. The geometrical constructions lifting tensor fields of type (0,2) on manifolds to the bundles of A -velocities, Nagoya Math. J., 140 (1995) (in press). Zbl0854.53018MR1369482
  9. Tangent and cotangent bundles, Marcel Dekker, INC. , New York, 1973. MR0350650

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