Green's theorem on a foliated Riemannian manifold and its applications
type: Item
instance of: scholarly article
title: Green's theorem on a foliated Riemannian manifold and its applications
zbMATH Open document ID: 0734.53028
DOI: 10.1007/BF01903838
author: N. E. Zubov
published in: Acta Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: The authors prove a q-codimensional analogue of the classical Green's theorem. For minimal foliations this implies that - with respect to the transverse Riemannian connection - those parallel normal vectorfields which are divergence-free and for which the Laplacian equals the Ricci operator must be transverse Killing.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4214862
zbMATH Keywords: bundle-like metrics
zbMATH Keywords: Green's theorem
zbMATH Keywords: minimal foliations
zbMATH Keywords: transverse Riemannian connection
zbMATH Keywords: parallel normal vectorfields
Wikidata QID: Q115393060
reviewed by: Grzegorz Andrzejczak
MaRDI profile type: Publication
cites work: Q3810468
cites work: Q5658761
cites work: Q3892996
cites work: Q3664067
cites work: Foliated manifolds with bundle-like metrics
cites work: The non-existence of Killing fields
cites work: \(A_{\nu}\)-operator on complete foliated Riemannian manifolds
description: scientific article; zbMATH DE number 4214862