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.

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关于实解析列维平坦超曲面和全纯网络

我们研究紧复杂曲面上与实解析列维平坦超曲面相切的全纯网。在某些条件下，我们证明与实解析列维平坦超曲面相切的全纯网允许多值亚纯第一积分。我们还证明了由格拉斯曼中不可约实解析曲线引起的列维平坦超曲面的列维叶状结构$G（n+1,n）$延伸到复射影空间上的代数网。