Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/108305
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Type: | Journal article |
Title: | Prolongation on contact manifolds |
Author: | Eastwood, M. Gover, A. |
Citation: | Indiana University Mathematics Journal, 2011; 60(5):1425-1485 |
Publisher: | Dept. of Mathematics, Indiana University |
Issue Date: | 2011 |
ISSN: | 0022-2518 |
Statement of Responsibility: | Michael Eastwood and A. Rod Gover |
Abstract: | On contact manifolds we describe a notion of (contact) finite type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite type in this sense but are not well understood by currently available techniques. We resolve this in the following sense. For any such D we construct a partial connection ∇H on a (finiterank) vector bundle with the property that sections in the null space of D correspond bijectively, and via an explicit map, with sections parallel for the partial connection. It follows that the solution space of D is finite dimensional and bounded by the corank of the holonomy algebra of ∇H. The treatment is via a uniformprocedure, even though in most cases no normal Cartan connection is available. |
Keywords: | Prolongation; partial differential equation; contact manifold |
Rights: | Indiana University Mathematics Journal © |
DOI: | 10.1512/iumj.2011.60.4980 |
Published version: | http://dx.doi.org/10.1512/iumj.2011.60.4980 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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RA_hdl_108305.pdf Restricted Access | Restricted Access | 491.11 kB | Adobe PDF | View/Open |
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