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On a canonical immersion of the A-jet manifolds into a Grassmann bundle


Abstract


For a given smooth manifold M we will consider the ideals I of \mathcal{C}^\infty(M) such that \mathcal{C}^\infty/I is a Weil algebra of order k; the set of these ideals is the disjoint union of several A-jets manifolds; by fixing \dim \mathcal{C}^\infty/I we will immerse the above mentioned set into a Grassmann bundle of the k-th cotangent bundle of M, explicitly showing the equations of such an immersion. Finally, in a particular case, we will see how the aforesaid A-jets manifolds are placed.


DOI Code: 10.1285/i15900932v20n2p115

Keywords: Jet; Contact element; Weil bundle; Grassmann bundle

Classification: 58A20

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