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Orbits and global unique continuation for systems of vector fields. (English) Zbl 0917.58004
Let \({\mathcal M}\) be a smooth, connected paracompact manifold and let \({\mathcal V}\) be a locally integrable vector subbundle of the complexified tangent bundle \(\mathbb{C} T{\mathcal M}\) of \({\mathcal M}\). The main purpose of the present paper is to explore the global unique continuation property of distribution solutions of \({\mathcal V}\), i.e., the distributions \(u\) on \({\mathcal M}\) such that \(Lu=0\) whenever \(L\) is a section of \({\mathcal V}\). More precisely, the authors are interested to determine conditions on \({\mathcal M}\) and/or the structure \({\mathcal V}\) such that if \(u\) is a solution on \({\mathcal M}\) that vanishes on an open subset of \({\mathcal M}\), then \(u\) vanishes on \({\mathcal M}\). The closely related problem of the structure of the Sussmann orbits of \({\mathbb{R}}\mathcal V\) is also studied in this paper.

MSC:
58A30 Vector distributions (subbundles of the tangent bundles)
32V99 CR manifolds
35N10 Overdetermined systems of PDEs with variable coefficients
58J99 Partial differential equations on manifolds; differential operators
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