On the nonexistence of CR functions on Levi-flat CR manifolds
type: Item
instance of: scholarly article
title: On the nonexistence of CR functions on Levi-flat CR manifolds
zbMATH Open document ID: 0783.32006
author: Takashi Inaba
published in: Collectanea Mathematica
publication date: 1993-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/41881
review text: 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)].
Mathematics Subject Classification ID: 32V99
zbMATH DE Number: 425617
zbMATH Keywords: Levi-flat CR manifold
zbMATH Keywords: CR function
zbMATH Keywords: Levi foliation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 425617