Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 297–316

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

Article

Abstract

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

We also introduce the space JA(M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space Jr(M,N).

Keywords

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

MSC 2010

58A20 58A32 53C24 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic

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