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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.

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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