Conditions on a Surface F² is subset of Eⁿ to lie in E⁴
We consider a surface F² in Eⁿ with a non-degenerate ellipse of normal curvature whose plane passes through the corresponding surface point. The definition of three types of points is given in dependence of the position of the point relatively to the ellipse. If in the domain D is subset of F² all t...
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| Date: | 2013 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2013
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106742 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Conditions on a Surface F² is subset of Eⁿ to lie in E⁴ / Yu.A. Aminov, Ia. Nasiedkina // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 2. — С. 127-149. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider a surface F² in Eⁿ with a non-degenerate ellipse of normal curvature whose plane passes through the corresponding surface point. The definition of three types of points is given in dependence of the position of the point relatively to the ellipse. If in the domain D is subset of F² all the points are of the same type, then the domain D is said also to be of this type. This classification of points and domains is linked with the classification of partial differential equations of the second order. The theorems on the surface to lie in E⁴ are proved under the fulfilment of certain boundary conditions. Some examples of the surfaces are constructed to show that the boundary conditions of the theorems are essential. |
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