On real submanifolds of Kähler manifolds foliated by complex submanifolds
type: Item
instance of: scholarly article
title: On real submanifolds of Kähler manifolds foliated by complex submanifolds
zbMATH Open document ID: 0798.53031
author: Takashi Inaba
author: Michael A. Mishchenko
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-08-08T00:00:00Z
review text: Let \(X\) be a Kähler manifold, \(M\) a compact orientable real submanifold of \(X\), and suppose that \(M\) admits a foliation \(\mathfrak F\) whose leaves are complex submanifolds of \(X\) with complex dimension \(p\). The authors prove that if the \(p\)-th power of the Kähler form of \(X\) is exact when restricted to \(M\), then \(\mathfrak F\) has no nontrivial foliation cycles. Some applications are given and it is stated that analogous results hold in symplectic and contact geometry.
reviewed by: Jürgen Berndt
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 597317
zbMATH Keywords: foliations by complex submanifolds
zbMATH Keywords: Kähler manifold
zbMATH Keywords: real submanifold
zbMATH Keywords: foliation
zbMATH Keywords: Kähler form
MaRDI profile type: Publication
full work available at URL: pjaa.70.1
OpenAlex ID: W1964671643
cites work: On the topology of compact smooth three-dimensional Levi-flat hypersurfaces
cites work: Foliations with measure preserving holonomy
cites work: Komplex-analytische Blätterung reeller Hyperflächen im \(C^n\)
cites work: Cycles for the dynamical study of foliated manifolds and complex manifolds
DOI: 10.3792/PJAA.70.1
description: scientific article; zbMATH DE number 597317