The general rigidity result for bundles of A -covelocities and A -jets

Jiří M. Tomáš

Czechoslovak Mathematical Journal (2017)

  • Issue: 2, page 297-316
  • ISSN: 0011-4642

Abstract

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Let M be an m -dimensional manifold and A = 𝔻 k r / I = N A a Weil algebra of height r . We prove that any A -covelocity T x A f T x A * M , x M is determined by its values over arbitrary max { width A , m } regular and under the first jet projection linearly independent elements of T x A M . 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 T r * M without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from m k to all cases of m . 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 ) .

How to cite

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Tomáš, Jiří M.. "The general rigidity result for bundles of $A$-covelocities and $A$-jets." Czechoslovak Mathematical Journal (2017): 297-316. <http://eudml.org/doc/288199>.

@article{Tomáš2017,
abstract = {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 \lbrace \mathop \{\rm width\}A, m \rbrace $ 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 $m$. 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 $J^r(M,N)$.},
author = {Tomáš, Jiří M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {$r$-jet; bundle functor; Weil functor; Lie group; jet group; $B$-admissible $A$-velocity},
language = {eng},
number = {2},
pages = {297-316},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The general rigidity result for bundles of $A$-covelocities and $A$-jets},
url = {http://eudml.org/doc/288199},
year = {2017},
}

TY - JOUR
AU - Tomáš, Jiří M.
TI - The general rigidity result for bundles of $A$-covelocities and $A$-jets
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 297
EP - 316
AB - 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 \lbrace \mathop {\rm width}A, m \rbrace $ 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 $m$. 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 $J^r(M,N)$.
LA - eng
KW - $r$-jet; bundle functor; Weil functor; Lie group; jet group; $B$-admissible $A$-velocity
UR - http://eudml.org/doc/288199
ER -

References

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