Hermitian metric rigidity on compact foliated manifolds
type: Item
instance of: scholarly article
title: Hermitian metric rigidity on compact foliated manifolds
zbMATH Open document ID: 0836.53019
DOI: 10.1007/BF01263487
author: R. Quiroga
published in: Geometriae Dedicata
publication date: 1996-04-16T00:00:00Z
review text: Some rigidity type results are obtained for a compact foliated manifold \((M, {\mathcal F})\) equipped with a leafwise holomorphic structure and a smooth leafwise Kähler metric \(g\). For example, if each leaf is uniformized by a fixed irreducible bounded symmetric domain \(\Omega\) of rank \(\geq 2\), \(h\) is a smooth leafwise Hermitian metric of non-positive curvature in the sense of Griffiths, then \(g\) and \(h\) are homothetic on \(\mu\)-a.e. leaf, \(\mu\) being a finite invariant transverse measure for \(\mathcal F\). Some applications of this result are provided.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 806291
zbMATH Keywords: foliation
zbMATH Keywords: rigidity
zbMATH Keywords: Hermitian metric
reviewed by: Paweł Walczak
MaRDI profile type: Publication
cites work: Foliated Plateau problem. II: Harmonic maps of foliations
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cites work: Geometric superrigidity
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description: scientific article; zbMATH DE number 806291