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Matematicheskie Zametki, 2013, Volume 94, Issue 2, Pages 163–174
DOI: https://doi.org/10.4213/mzm6347 (Mi mzm6347) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Conditions for a Two-Dimensional Surface in $E^5$ to Be Contained in a Hypersphere or a Hyperplane

Yu. A. Aminov, Ya. S. Nasedkina

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
Full-text PDF (476 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm6347
Abstract: Two theorems on conditions under which a two-dimensional surface in Euclidean 5-space is contained in a hypersphere and one theorem on conditions under which such a surface is contained in a hyperplane are proved. The notion of hyperbolic and elliptic domains on a surface are introduced. The conditions in the theorems are expressed in terms of the behavior of the plane of the normal curvature ellipse of the surface and certain boundary conditions. An example which shows that the boundary conditions are essential is constructed.
Keywords: hyperspherical surface, hyperplanar surface, ellipse of normal curvature, hyperbolic domain, elliptic domain, parabolic domain.
Received: 12.10.2008
Revised: 25.04.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 2, Pages 167–176
DOI: https://doi.org/10.1134/S000143461307016X
Bibliographic databases:
Document Type: Article
UDC: 514.76
Language: Russian
Citation: Yu. A. Aminov, Ya. S. Nasedkina, “Conditions for a Two-Dimensional Surface in $E^5$ to Be Contained in a Hypersphere or a Hyperplane”, Mat. Zametki, 94:2 (2013), 163–174; Math. Notes, 94:2 (2013), 167–176
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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