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On the nonexistence of CR functions on Levi-flat CR manifolds.

Takashi Inaba (1992)

Collectanea Mathematica

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.

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

Let X 1 and X 2 be two compact strongly pseudoconvex CR manifolds of dimension 2 n - 1 5 which bound complex varieties V 1 and V 2 with only isolated normal singularities in N 1 and N 2 respectively. Let S 1 and S 2 be the singular sets of V 1 and V 2 respectively and S 2 is nonempty. If 2 n - N 2 - 1 1 and the cardinality of S 1 is less than 2 times the cardinality of S 2 , then we prove that any non-constant CR morphism from X 1 to X 2 is necessarily a CR biholomorphism. On the other hand, let X be a compact strongly pseudoconvex CR manifold of...

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