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.