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Uspekhi Mat. Nauk, 1973, Volume 28, Issue 4(172), Pages 47–76 (Mi umn4921)  

This article is cited in 10 scientific papers (total in 10 papers)

Isometric immersions of two-dimensional Riemannian metrics in euclidean space

È. G. Poznyak


Abstract: In this paper we consider the problem of global isometric immersions of two-dimensional Riemannian metrics in Euclidean space. The dimension of the ambient space depends on the character of the Riemannian metric in question.

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English version:
Russian Mathematical Surveys, 1973, 28:4, 47–77

Bibliographic databases:

UDC: 513.8
MSC: 53A05, 53C42, 53C25, 53C21
Received: 23.04.1973

Citation: È. G. Poznyak, “Isometric immersions of two-dimensional Riemannian metrics in euclidean space”, Uspekhi Mat. Nauk, 28:4(172) (1973), 47–76; Russian Math. Surveys, 28:4 (1973), 47–77

Citation in format AMSBIB
\Bibitem{Poz73}
\by \`E.~G.~Poznyak
\paper Isometric immersions of two-dimensional Riemannian metrics in euclidean space
\jour Uspekhi Mat. Nauk
\yr 1973
\vol 28
\issue 4(172)
\pages 47--76
\mathnet{http://mi.mathnet.ru/umn4921}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=394514}
\zmath{https://zbmath.org/?q=an:0283.53001|0289.53004}
\transl
\jour Russian Math. Surveys
\yr 1973
\vol 28
\issue 4
\pages 47--77
\crossref{https://doi.org/10.1070/RM1973v028n04ABEH001591}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Chang-Shou Lin, “The local isometric embedding inR3 of two-dimensional Riemannian manifolds with Gaussian curvature changing sign cleanly”, Comm Pure Appl Math, 39:6 (1986), 867  crossref  mathscinet  isi
    2. T. Klotts-Milnor, “Teorema Efimova o polnykh pogruzhennykh poverkhnostyakh otritsatelnoi krivizny”, UMN, 41:5(251) (1986), 3–57  mathnet  mathscinet  zmath
    3. A. A. Borisenko, “Isometric immersions of space forms into Riemannian and pseudo-Riemannian spaces of constant curvature”, Russian Math. Surveys, 56:3 (2001), 425–497  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. A. Aminov, “Extrinsic geometric properties of the Rozendorn surface, an isometric immersion of the Lobachevskiǐ plane in $E^5$”, Sb. Math., 200:11 (2009), 1575–1586  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Emil Saucan, “Isometric Embeddings in Imaging and Vision: Facts and Fiction”, J Math Imaging Vis, 2011  crossref
    6. J A Gemmer, S C Venkataramani, “Defects and boundary layers in non-Euclidean plates”, Nonlinearity, 25:12 (2012), 3553  crossref
    7. Malykin G.B., “Metod E. Borelya dlya vychisleniya pretsessii tomasa. Geometricheskaya faza v relyativistskom kinematicheskom prostranstve skorostei i ee prilozheniya v optike”, Optika i spektroskopiya, 114:2 (2013), 293–293  elib
    8. John Gemmer, Sh.C.. Venkataramani, “Shape transitions in hyperbolic non-Euclidean plates”, Soft Matter, 9:34 (2013), 8151  crossref
    9. Mirandola H. Vitorio F., “Global Isometric Embeddings of Multiple Warped Product Metrics Into Quadrics”, 38, no. 1, 2015, 119–134  isi
    10. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Успехи математических наук Russian Mathematical Surveys
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