The general rigidity result for bundles of $A$-covelocities and $A$-jets
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 297-316
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 $J^r(M,N)$.
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 $J^r(M,N)$.
DOI :
10.21136/CMJ.2017.0566-15
Classification :
53C24, 58A20, 58A32
Keywords: $r$-jet; bundle functor; Weil functor; Lie group; jet group; $B$-admissible $A$-velocity
Keywords: $r$-jet; bundle functor; Weil functor; Lie group; jet group; $B$-admissible $A$-velocity
@article{10_21136_CMJ_2017_0566_15,
author = {Tom\'a\v{s}, Ji\v{r}{\'\i}},
title = {The general rigidity result for bundles of $A$-covelocities and $A$-jets},
journal = {Czechoslovak Mathematical Journal},
pages = {297--316},
year = {2017},
volume = {67},
number = {2},
doi = {10.21136/CMJ.2017.0566-15},
mrnumber = {3661042},
zbl = {06738520},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0566-15/}
}
TY - JOUR AU - Tomáš, Jiří TI - The general rigidity result for bundles of $A$-covelocities and $A$-jets JO - Czechoslovak Mathematical Journal PY - 2017 SP - 297 EP - 316 VL - 67 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0566-15/ DO - 10.21136/CMJ.2017.0566-15 LA - en ID - 10_21136_CMJ_2017_0566_15 ER -
%0 Journal Article %A Tomáš, Jiří %T The general rigidity result for bundles of $A$-covelocities and $A$-jets %J Czechoslovak Mathematical Journal %D 2017 %P 297-316 %V 67 %N 2 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0566-15/ %R 10.21136/CMJ.2017.0566-15 %G en %F 10_21136_CMJ_2017_0566_15
Tomáš, Jiří. The general rigidity result for bundles of $A$-covelocities and $A$-jets. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 297-316. doi: 10.21136/CMJ.2017.0566-15
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