{"paper":{"title":"Remarks on non-maximal integral elements of the Cartan plane in jet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G. Moreno, M. J. Baechtold","submitted_at":"2012-08-29T11:15:25Z","abstract_excerpt":"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-Am"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5880","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}