On the nonexistence of CR functions on Levi-flat CR manifolds
We show that no compact Levi-flat CR manifold of CR codimension one admits a continuous CR function which is nonconstant along leaves of the Levi foliation. We also prove the nonexistence of certain CR functions on a neighborhood of a compact leaf of some Levi-flat CR 3-manifolds, and apply it to showing that some foliated 3-manifolds cannot be embedded as smooth Levi-flat real hypersurfaces in complex surfaces. For related results see \textit{D. E. Barrett} [Math. Z. 203, 355-361 (1990; Zbl 0662.57015)] and \textit{D. E. Barrett} and the author [J. Geom. Anal. 2, No. 6, 489-497 (1992; Zbl 0762.32014)].
scientific article; zbMATH DE number 425617