Small parameter in the theory of isometric imbeddings for two-dimensional Riemannian manifolds into Euclidean spaces
type: Item
instance of: scholarly article
title: Small parameter in the theory of isometric imbeddings for two-dimensional Riemannian manifolds into Euclidean spaces
zbMATH Open document ID: 0849.53041
DOI: 10.1007/BF02362833
author: E. V. Shikin
author: Eh. G. Poznyak
published in: Journal of Mathematical Sciences (New York)
publication date: 1996-11-10T00:00:00Z
review text: The article presents a survey of research papers of the authors and of J. Kajdasov, C. S. Lin, G. Nakamura, B. L. Rozhdestvenskij, D. V. Tunitskij a.o. Chapter headings are: 1. Numerical parameter in the isometric imbedding problems of the negative-curvature manifolds into the Euclidean space \(E^3\). 2. A small functional parameter in the imbedding problems of manifolds with negative curvature. 3. A small parameter in the sine-Gordon equation. 4. The isometric imbedding of two-dimensional manifolds into the four-dimensional Euclidean space. 5. A small parameter in the isometric imbedding problems for analytic metrics. 6. Application of a small parameter for the imbedding of two-dimensional manifolds of curvature with alternating signs.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 53-02
zbMATH DE Number: 877643
zbMATH Keywords: isometric imbedding into Euclidean space
zbMATH Keywords: negative curvature
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: analytic metrics
Wikidata QID: Q115392402
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02362833
OpenAlex ID: W2065296952
description: scientific article; zbMATH DE number 877643