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This article is cited in 11 scientific papers (total in 11 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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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
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\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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http://mi.mathnet.ru/eng/umn4921 http://mi.mathnet.ru/eng/umn/v28/i4/p47
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This publication is cited in the following articles:
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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
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T. Klotts-Milnor, “Teorema Efimova o polnykh pogruzhennykh poverkhnostyakh
otritsatelnoi krivizny”, UMN, 41:5(251) (1986), 3–57
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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
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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
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Emil Saucan, “Isometric Embeddings in Imaging and Vision: Facts and Fiction”, J Math Imaging Vis, 2011
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J A Gemmer, S C Venkataramani, “Defects and boundary layers in non-Euclidean plates”, Nonlinearity, 25:12 (2012), 3553
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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
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John Gemmer, Sh.C.. Venkataramani, “Shape transitions in hyperbolic non-Euclidean plates”, Soft Matter, 9:34 (2013), 8151
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Mirandola H. Vitorio F., “Global Isometric Embeddings of Multiple Warped Product Metrics Into Quadrics”, 38, no. 1, 2015, 119–134
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I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
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Aminov Yu.A., “Two-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean Spaces. Results and Unsolved Problems”, Ukr. Math. J., 71:1 (2019), 1–38
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