On real-analytic Levi-flat hypersurfaces and holomorphic webs. (English) Zbl 1537.32135
Summary: We investigate holomorphic webs tangent to real-analytic Levi-flat hypersurfaces on compact complex surfaces. Under certain conditions, we prove that a holomorphic web tangent to a real-analytic Levi-flat hypersurface admits a multiple-valued meromorphic first integral. We also prove that the Levi foliation of a Levi-flat hypersurface induced by an irreducible real-analytic curve in the Grassmannian \(G(n+1, n)\) extends to an algebraic web on the complex projective space.
MSC:
| 32V40 | Real submanifolds in complex manifolds |
| 32M25 | Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions |
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