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Let M be an m-dimensional manifold and A = D k   r /I = R⊕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.

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