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Matematicheskie Zametki, 2015, Volume 98, Issue 3, Pages 378–385
DOI: https://doi.org/10.4213/mzm10815 (Mi mzm10815) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Isometric Embeddings in $\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type

S. N. Mikhalev, I. Kh. Sabitov

Lomonosov Moscow State University
Full-text PDF (506 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10815
Abstract: It is proved that a locally Euclidean metric on a circular annulus admitting an isometric immersion in $\mathbb R^2$ which is multivalued of cylindrical type can be isometrically embedded in $\mathbb R^3$ as a cylindrical surface.
Keywords: locally Euclidean metric, isometric embedding, isometric immersion, cylindrical surface, planar graph.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-90415-Укр_а
This work was supported in part by the Russian Foundation for Basic Research under grant 12-01-90415-Ukr_a.
Received: 25.02.2014
Revised: 19.03.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 3, Pages 441–447
DOI: https://doi.org/10.1134/S0001434615090096
Bibliographic databases:
Document Type: Article
UDC: 515.14
Language: Russian
Citation: S. N. Mikhalev, I. Kh. Sabitov, “Isometric Embeddings in $\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type”, Mat. Zametki, 98:3 (2015), 378–385; Math. Notes, 98:3 (2015), 441–447
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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