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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm6347https://doi.org/10.4213/mzm6347 https://www.mathnet.ru/eng/mzm/v94/i2/p163
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Abstract page: | 589 | Full-text PDF : | 180 | References: | 71 | First page: | 31 |
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