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Global analytic regularity for structures of co-rank one. (English) Zbl 1153.35006
The authors consider a real analytic involutive structure $${\mathcal V}$$, of co-rank one, defined on a real analytic paracompact orientable manifold $$M$$. To such a structure certain connected sets (called level sets of $${\mathcal V}$$) are associated. The authors prove that analytic regularity propagates along them. With further assumptions on the level sets the global analytic hypoellipticity of a differential operator naturally associated to $${\mathcal V}$$ is characterized. An application is given to the case of tube structures.

##### MSC:
 35A21 Singularity in context of PDEs 35H10 Hypoelliptic equations 35B65 Smoothness and regularity of solutions to PDEs
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##### References:
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