|
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.
 Full text:
PDF file (1849 kB)
References:
PDF file
HTML file
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}
Linking options:
http://mi.mathnet.ru/eng/umn4921 http://mi.mathnet.ru/eng/umn/v28/i4/p47
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:
-
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
 -
T. Klotts-Milnor, “Teorema Efimova o polnykh pogruzhennykh poverkhnostyakh
otritsatelnoi krivizny”, UMN, 41:5(251) (1986), 3–57
 -
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
 -
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
 -
Emil Saucan, “Isometric Embeddings in Imaging and Vision: Facts and Fiction”, J Math Imaging Vis, 2011
-
J A Gemmer, S C Venkataramani, “Defects and boundary layers in non-Euclidean plates”, Nonlinearity, 25:12 (2012), 3553
-
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
-
John Gemmer, Sh.C.. Venkataramani, “Shape transitions in hyperbolic non-Euclidean plates”, Soft Matter, 9:34 (2013), 8151
-
Mirandola H. Vitorio F., “Global Isometric Embeddings of Multiple Warped Product Metrics Into Quadrics”, 38, no. 1, 2015, 119–134
-
I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
|
| Number of views: |
| This page: | 395 | | Full text: | 183 | | References: | 37 | | First page: | 2 |
|
Terms of Use