The geometry of totally geodesic Riemannian foliations
type: Item
instance of: scholarly article
title: The geometry of totally geodesic Riemannian foliations
zbMATH Open document ID: 1034.53026
author: A. Y. Narmanov
published in: Russian Mathematics
publication date: 2001-03-07T00:00:00Z
review text: Let \(\mathcal F\) be a totally geodesic, Riemannian foliation of a complete Riemannian manifold \(M\). Let \(H\) be the orthogonal complement to the distribution \(T{\mathcal F}\). The author defines a metric connection \(\tilde \nabla\) on \(M\) for which both \(T{\mathcal F}\) and \(H\) are parallel. The distribution \(H\) is integrable if and only if \(\tilde \nabla\) is torsion--free.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1541525
zbMATH Keywords: totally geodesic foliation
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: Ehresmann connection
reviewed by: James Hebda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541525