| Title:
|
The general rigidity result for bundles of $A$-covelocities and $A$-jets (English) |
| Author:
|
Tomáš, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
297-316 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M$ be an $m$-dimensional manifold and $A=\mathbb D^r_k /I=\mathbb R \oplus N_A$ a Weil algebra of height $r$. We prove that any $A$-covelocity $T^A_x f \in T^{A*}_x M$, $x \in M$ is determined by its values over arbitrary $\max \{\mathop {\rm width}A, m \}$ regular and under the first jet projection linearly independent elements of $T^A_xM$. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result $T^{A*}M \simeq T^{r*}M$ without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from $m \ge k$ to all cases of $m$. \endgraf We also introduce the space $J^A(M,N)$ of $A$-jets and prove its rigidity in the sense of its coincidence with the classical jet space $J^r(M,N)$. (English) |
| Keyword:
|
$r$-jet |
| Keyword:
|
bundle functor |
| Keyword:
|
Weil functor |
| Keyword:
|
Lie group |
| Keyword:
|
jet group |
| Keyword:
|
$B$-admissible $A$-velocity |
| MSC:
|
53C24 |
| MSC:
|
58A20 |
| MSC:
|
58A32 |
| idZBL:
|
Zbl 06738520 |
| idMR:
|
MR3661042 |
| DOI:
|
10.21136/CMJ.2017.0566-15 |
| . |
| Date available:
|
2017-06-01T14:24:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146757 |
| . |
| Reference:
|
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