Partial extensions of jets and the polar distribution on Gras smannians of non-maximal integral elements

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Baechtold, Michael¹ 

[1] Lucerne Univ Appl Sci & Arts, Technikumstr 21, CH-6048 Horw, Switzerland

关键词: Jet spaces;    Exterior differential systems;    Geometry of PDEs;   

DOI  :  10.1016/j.jde.2015.10.028

来源: Elsevier

【 摘 要 】

We study an intrinsic distribution, called polar, on the space of 1-dimensional integral elements of the higher order contact structure on jet spaces. The main result establishes that this exterior differential system is the prolongation of a natural system of PDEs, named pasting conditions, on sections of the bundle of partial jet extensions. Informally, a partial jet extension is a kth order jet with additional (k + 1)st order information along 1 of then possible directions. A choice of partial extensions of a jet into all possible l-directions satisfies the pasting conditions if the extensions coincide along pairwise intersecting l-directions. We further show that prolonging the polar distribution once more yields the space of (1, n)-dimensional integral flags with its double fibration distribution. When l > 1 the exterior differential system is holonomic, stabilizing after one further prolongation. The proof starts form the space of integral flags, constructing the tower of prolongations by reduction. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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