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arXiv · 1208.5880

Remarks on non-maximal integral elements of the Cartan plane in jet spaces

M. J. Baechtold·G. Moreno
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Abstract

There is a natural filtration on the space of degree-$k$ homogeneous polynomials in $n$ independent variables with coefficients in the algebra of smooth functions on the Grassmannian $\mathrm{Gr}(n,s)$, determined by the tautological bundle. In this paper we show that the space of $s$-dimensional integral elements of a Cartan plane on $J^{k-1}(E,n)$, with $\mathrm{dim}\, E=n+m$, has an affine bundle structure modeled by the the so-obtained bundles over $\mathrm{Gr}(n,s)$, and we study a natural distribution associated with it. As an example, we show that a third-order nonlinear PDE of Monge-Amp\`ere type is not contact-equivalent to a quasi-linear one.

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M. J. Baechtold, G. Moreno. 2012-08-29. Remarks on non-maximal integral elements of the Cartan plane in jet spaces. https://arxiv.org/abs/1208.5880

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