\(\lambda\)-automorphisms of a Riemannian foliation
type: Item
instance of: scholarly article
title: \(\lambda\)-automorphisms of a Riemannian foliation
zbMATH Open document ID: 0830.53025
DOI: 10.1007/BF00773660
author: Hong Kyung Pak
published in: Annals of Global Analysis and Geometry
publication date: 1995-10-09T00:00:00Z
review text: The notion of \(\lambda\)-automorphisms \((\lambda \in \mathbb{R})\) of a Riemannian foliation \(\mathcal F\) on a manifold \(M\) was introduced first by \textit{F. W. Kamber, Ph. Tondeur} and \textit{G. Toth} in the paper ``Transversal Jacobi fields for harmonic foliations'' [Mich. Math. J. 34, 261-266 (1987; Zbl 0629.53031)]. Briefly speaking, such \(\lambda\)- automorphisms are sections \(s\) of the normal bundle \(Q = TM/T{\mathcal F}\) which satisfy a particular differential equation involving \(\lambda\), the Laplace operator in \(Q\), the transverse Levi-Civita connection, the transverse divergence, etc. Here, several identities for \(\lambda\)- automorphisms are derived. Also, some geometrical conditions sufficient for a \(\lambda\)-automorphism \(s\) to be either transversely Killing or transversely conformal are given.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 792879
zbMATH Keywords: Riemannian foliations
zbMATH Keywords: \(\lambda\)-automorphism
zbMATH Keywords: generalized transversal Jacobi operator
zbMATH Keywords: transverse Killing field
zbMATH Keywords: transverse conformal field
reviewed by: Paweł Walczak
MaRDI profile type: Publication
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Wikidata QID: Q115394878
full work available at URL: https://doi.org/10.1007/bf00773660
OpenAlex ID: W4236076157
description: scientific article; zbMATH DE number 792879