| Title:
|
Liftings of $1$-forms to the linear $r$-tangent bundle (English) |
| Author:
|
Mikulski, W. M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
97-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $T^*\rightarrow T^{r*}$. (English) |
| Keyword:
|
linear r-tangent bundle |
| Keyword:
|
linear natural operator |
| Keyword:
|
1-form |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0844.58006 |
| idMR:
|
MR1357978 |
| . |
| Date available:
|
2008-06-06T21:28:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107530 |
| . |
| Reference:
|
[1] Doupovec, M., Kurek, J.: Liftings of covariant $(0,2)$-tensor fields to the bundle of $k$-dimensional $1$-velocities.Suppl. Rend. Circ. Mat. Palermo (in press). |
| Reference:
|
[2] Gancarzewicz, J., Mahi, S.: Liftings of 1-forms to the tangent bundle of higher order.Czech. Math. J. 40 (115) (1990), 397–407. MR 1065019 |
| Reference:
|
[3] Jany¨ka, J.: Natural operations with projectable tangent valued forms on fibered manifolds.Annali di Math. CLIX (1991), 171–184. |
| Reference:
|
[4] Kol ©, I., Michor, P. W., Slov k, J.: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[5] Kurek, J.: On the first order natural operators transforming 1-forms on a manifold to linear frame bundle.Demonstratio Math. 26 (1993), 287–293. MR 1240218 |
| Reference:
|
[6] Kurek, J.: 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. Zbl 0739.58001, MR 1158100 |
| Reference:
|
[7] Mikulski, W. M.: The natural operators lifting 1-forms on manifolds to the bundles of $A$-velocities.Mh. Math., 119 (1995), 63–77. Zbl 0823.58004, MR 1315684 |
| Reference:
|
[8] Mikulski, W. M.: 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). Zbl 0854.53018, MR 1369482 |
| Reference:
|
[9] Yano, K., Ishihara, S.: Tangent and cotangent bundles.Marcel Dekker, INC. , New York, 1973. MR 0350650 |
| . |
