Riemannian foliations on manifolds with non-negative curvature
type: Item
instance of: scholarly article
title: Riemannian foliations on manifolds with non-negative curvature
zbMATH Open document ID: 0763.53036
DOI: 10.1007/BF02567656
author: Hobum Kim
author: Philippe Tondeur
published in: Manuscripta Mathematica
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/155681
review text: Any Riemannian foliation \(\mathcal F\) of a complete Riemannian manifold \(M\) (with bundle-like metric) is shown to be totally geodesic provided that the partial Ricci curvature \(R^ L\) of \(M\) (in the direction of \(\mathcal F\)) is non-negative and the norm of the second fundamental form of \(\mathcal F\) is bounded by a constant which depends on codim\(\mathcal F\) and the lower bound for \(R^ L\). Some immediate Corollaries are formulated.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 60085
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: totally geodesic
zbMATH Keywords: Ricci curvature
zbMATH Keywords: second fundamental form
Wikidata QID: Q115392026
reviewed by: Paweł Walczak
MaRDI profile type: Publication
cites work: Applications of a Riccati type differential equation to Riemannian manifolds with totally geodesic distributions
cites work: Totally geodesic foliations
cites work: An Example Relevant to Curvature Pinching Theorems for Riemannian Foliations
cites work: Curvature properties of harmonic foliations
cites work: The fundamental equations of a submersion
cites work: Submersions and geodesics
cites work: On a remark of O'Neill
cites work: Foliated manifolds with bundle-like metrics
cites work: Q4743396
OpenAlex ID: W2061263431
description: scientific article; zbMATH DE number 60085