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.
@article{urn:eudml:doc:41881,
title = {On the nonexistence of CR functions on Levi-flat CR manifolds.},
journal = {Collectanea Mathematica},
volume = {43},
year = {1992},
pages = {83-87},
zbl = {0783.32006},
mrnumber = {MR1214226},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41881}
}
Inaba, Takashi. On the nonexistence of CR functions on Levi-flat CR manifolds.. Collectanea Mathematica, Tome 43 (1992) pp. 83-87. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41881/