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Журнал математической физики, анализа, геометрии, 2013, том 9, номер 2, страницы 127–149
(Mi jmag553)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Conditions on a Surface $F^2\subset E^n$ to lie in $E^4$
Yu. A. Aminov, Ia. Nasedkina Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
Аннотация:
We consider a surface $F^2$ in $E^n$ 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 $D\subset F^2$ 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 $E^4$ 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.
Ключевые слова и фразы:
an ellipse of normal curvature, asymptotic lines, characteristics, boundary conditions.
Поступила в редакцию: 30.05.2011 Исправленный вариант: 30.01.2012
Образец цитирования:
Yu. A. Aminov, Ia. Nasedkina, “Conditions on a Surface $F^2\subset E^n$ to lie in $E^4$”, Журн. матем. физ., анал., геом., 9:2 (2013), 127–149
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag553 https://www.mathnet.ru/rus/jmag/v9/i2/p127
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Страница аннотации: | 349 | PDF полного текста: | 109 | Список литературы: | 49 |
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