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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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