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Mat. Zametki, 2013, Volume 94, Issue 2, Pages 163–174 (Mi mz6347)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/mzm6347

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English version:
Mathematical Notes, 2013, 94:2, 167–176

Bibliographic databases:

UDC: 514.76
Received: 12.10.2008
Revised: 25.04.2012

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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  • http://mi.mathnet.ru/eng/mz/v94/i2/p163

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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. Nasedkina Ya.S., “Conditions Under Which a Submanifold $F^n$ from $E^{n+p}$ Belongs to $E^{2n-1}$”, Ukr. Math. J., 68:3 (2016), 399–405  crossref  mathscinet  isi  scopus
  • Математические заметки Mathematical Notes
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