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Global solvability of real analytic involutive systems on compact manifolds. II. (English) Zbl 1418.35002
The authors continue their previous study [Math. Ann. 369, No. 3–4, 1177–1209 (2017; Zbl 1380.35129)] on the global solvability of a locally integrable structure of tube type and a corank one, considering a linear partial differential operator \(\mathbb{L}\) associated with a real analytic closed 1-form defined on a real analytic closed \(n\)-manifold. The authors characterize the global hypoellipticity of \(\mathbb{L}\) and the global solvability of \(\mathbb{L}^{n-1}\).

MSC:
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35N10 Overdetermined systems of PDEs with variable coefficients
58J10 Differential complexes
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