On the perturbation problem associated to isometric embeddings of Riemannian manifolds
type: Item
instance of: scholarly article
title: On the perturbation problem associated to isometric embeddings of Riemannian manifolds
zbMATH Open document ID: 0691.53006
DOI: 10.1007/BF00137403
author: M. Günther
published in: Annals of Global Analysis and Geometry
publication date: 1989-01-01T00:00:00Z
review text: In the classical problem of isometric embedding of a Riemannian manifold into Euclidean space \({\mathbb{R}}^ q\) first, an ``almost'' isometric embedding is constructed, and then a special system of differential equations is solved for the ``correction'' term. The second step relies to the hard implicit function theorem (IFT) of Moser-Nash. In this article the author suggests a modified version of the system of equations for the ``correction'' term. For this system one can avoid using hard IFT.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 4131176
zbMATH Keywords: correction term
zbMATH Keywords: isometric embedding
zbMATH Keywords: differential equations
zbMATH Keywords: implicit function theorem
Wikidata QID: Q115395198
reviewed by: Vladimir I. Oliker
MaRDI profile type: Publication
cites work: Partial Differential Relations
cites work: Q5599507
cites work: The inverse function theorem of Nash and Moser
cites work: The boundary problems of physical geodesy
cites work: Champs spinoriels et propagateurs en relativité générale
cites work: Q5520417
cites work: The imbedding problem for Riemannian manifolds
cites work: Generalized implicit function theorems with applications to some small divisor problems, I
full work available at URL: https://doi.org/10.1007/bf00137403
OpenAlex ID: W2077047537
description: scientific article; zbMATH DE number 4131176