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

Czechoslovak Mathematical Journal

Jiří Tomáš¹ 

关键词: $r$-jet;    bundle functor;    Weil functor;    Lie group;    jet group;    $B$-admissible $A$-velocity;   

DOI  :  10.21136/CMJ.2017.0566-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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 $m$.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 $J^r(M,N)$.

【 授权许可】

Unknown