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

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.