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

作者：Tomas Jiri^*

来源：Czechoslovak Mathematical Journal, 2017, 67(2): 297-316.

DOI：10.21136/CMJ.2017.0566-15

• r-jet
• bundle functor
• Weil functor
• Lie group
• jet group
• B-admissible A-velocity

Let M be an m-dimensional manifold and A = D (k) (r) /I = RaS center dot N (A) a Weil algebra of height r. We prove that any A-covelocity T (x) (A) f a T (x) (A) *M, x a 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 ae integral T (r) *M without coordinate computations, which improves and generalizes the partial result obtained in Toma (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).

• 出版日期2017-6