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

Inaba, Takashi. "On the nonexistence of CR functions on Levi-flat CR manifolds.." Collectanea Mathematica 43.1 (1992): 83-87. <http://eudml.org/doc/41881>.

@article{Inaba1992,
abstract = {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.},
author = {Inaba, Takashi},
journal = {Collectanea Mathematica},
keywords = {Variedades topológicas; 3-variedades; Superficies Riemann; Foliaciones; Ideal maximal; Levi-flat CR manifold; CR function; Levi foliation},
language = {eng},
number = {1},
pages = {83-87},
title = {On the nonexistence of CR functions on Levi-flat CR manifolds.},
url = {http://eudml.org/doc/41881},
volume = {43},
year = {1992},
}

TY - JOUR
AU - Inaba, Takashi
TI - On the nonexistence of CR functions on Levi-flat CR manifolds.
JO - Collectanea Mathematica
PY - 1992
VL - 43
IS - 1
SP - 83
EP - 87
AB - 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.
LA - eng
KW - Variedades topológicas; 3-variedades; Superficies Riemann; Foliaciones; Ideal maximal; Levi-flat CR manifold; CR function; Levi foliation
UR - http://eudml.org/doc/41881
ER -