| Title:
|
Linear liftings of skew-symmetric tensor fields to Weil bundles (English) |
| Author:
|
Dębecki, Jacek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
809-816 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define equivariant tensors for every non-negative integer $p$ and every Weil algebra $A$ and establish a one-to-one correspondence between the equivariant tensors and linear natural operators lifting skew-symmetric tensor fields of type $(p,0)$ on an $n$-dimensional manifold $M$ to tensor fields of type $(p,0)$ on $T^AM$ if $1\le p\le n$. Moreover, we determine explicitly the equivariant tensors for the Weil algebras ${\mathbb D}^r_k$, where $k$ and $r$ are non-negative integers. (English) |
| Keyword:
|
natural operator |
| Keyword:
|
product preserving bundle functor |
| Keyword:
|
Weil algebra |
| MSC:
|
53A55 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 1081.53015 |
| idMR:
|
MR2153104 |
| . |
| Date available:
|
2009-09-24T11:27:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128024 |
| . |
| Reference:
|
[1] J. Gancarzewicz, W. Mikulski and Z. Pogoda: Lifts of some tensor fields and connections to product preserving functors.Nagoya Math. J. 135 (1994), 1–41. MR 1295815, 10.1017/S0027763000004931 |
| Reference:
|
[2] J. Grabowski and P. Urbański: Tangent lifts of Poisson and related structures.J. Phys. A 28 (1995), 6743–6777. MR 1381143, 10.1088/0305-4470/28/23/024 |
| Reference:
|
[3] P. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993. MR 1202431 |
| Reference:
|
[4] M. Mikulski: Natural transformations transforming functions and vector fields to functions on some natural bundles.Math. Bohem. 117 (1992), 217–223. Zbl 0810.58004, MR 1165899 |
| Reference:
|
[5] W. M. Mikulski: The linear natural operators lifting 2-vector fields to some Weil bundles.Note Mat. 19 (1999), 213–217. Zbl 1008.58004, MR 1816875 |
| . |
