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On bundles of covelocities

  • Jiří M. Tomáš
Article
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Abstract

For a Weil algebra A = \( \mathbb{D}\) r k /I = ℝ ⊕ N A and a manifold M satisfying dimM = mk, the coincidence of the space T A *M of A-covelocities T x A f: T x A MT 0 A ℝ with the bundle of the r-th order covelocities T r *M is proved. For a Lie subgroup G A G m r of I-preserving \( \mathbb{D}\) m r -automorphisms and a Lie group homomorphism p: G m r G A it is proved that the space T V,p A *M of T x A f restricted to individual regular p(G m r )-orbits on T m r M together with the extensions to other regular p(G m r )-orbits coincides with the natural bundle P r M[N A , ℓ] with the standard fiber N A and the left action ℓ: G m r × N A N A induced by p.

Key words and phrases

Lie group r-jet bundle functor Weil functor 

2000 Mathematics Subject Classification

58A20 58A32 58D15 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • Jiří M. Tomáš

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