Universal Prolongation of Linear Partial Differential Equations on Filtered Manifolds

Details Universal Prolongation of Linear Partial Differential Equations on Filtered Manifolds Universal Prolongation of Linear Partial Differential Equations on Filtered Manifolds

2009-04-16

arxiv.org/abs/0904.2519v3

Mathematics

Differential Geometry

14 pages; v3: minor changes in section 3, typos corrected; final version to appear in Arch. math (Brno) 5, 2009

Scientific paper

The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.

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