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\(\bar\partial\)-regularity for weakly pseudoconvex domains in compact Hermitian symmetric spaces with respect to invariant metrics. (English) Zbl 1030.53071
The following conjecture is proved: Main Theorem. Let \(q\geq 8\). Then there are no \(C^q\) Levi-flat real hypersurface \(M\) in \(\mathbb{P}_2\). (Here the Levi-flatness of \(M\) means that \(M\) is foliated by local complex-analytic curves.).

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C35 Differential geometry of symmetric spaces
53C12 Foliations (differential geometric aspects)
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