Riemannian foliations of bounded geometry
type: Item
instance of: scholarly article
title: Riemannian foliations of bounded geometry
zbMATH Open document ID: 1304.53020
author: Jesús A. Álvarez López
author: Eric Leichtnam
author: Yuri A. Kordyukov
published in: Mathematische Nachrichten
publication date: 2014-11-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.0637
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 6368929
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: bounded geometry
zbMATH Keywords: O'Neill tensors
MaRDI profile type: Publication
OpenAlex ID: W2963194908
Wikidata QID: Q115405898
arXiv ID: 1308.0637
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DOI: 10.1002/MANA.201300211
review text: A Riemannian foliation \(\mathcal{F}\) of a Riemannian manifold \((N, g)\) is said to have \textit{bounded geometry} whenever the norms of all the covariant derivatives of the curvature tensor \(R\) and of the O'Neill tensors \(T\) and \(A\) are bounded on \(N\). It is shown that then (1) all the leaves of \(\mathcal{F}\) have bounded geometry in the usual sense, (2) \(N\) can be covered by normal foliation charts for which the coordinates of the Riemannian tensor \(g\) lie in a bounded subset of the Fréchet space of the \(C^\infty\)-functions.
reviewed by: Paweł Walczak
description: scientific article; zbMATH DE number 6368929