Email this article A generalized theorem on curvilinear three-web boundaries and its applications
- Authors: Shelekhov A.M.1
-
Affiliations:
- Moscow State Pedagogical University
- Issue: Vol 211, No 3 (2020)
- Pages: 124-157
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133319
- DOI: https://doi.org/10.4213/sm9167
- ID: 133319
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Abstract
Suppose that a curvilinear three-web is given by the equation $F(x,y,z)=0$. A specific structure of the derivatives of the function $F$ is established that characterizes regular three-webs. This makes it possible to list all regular three-webs formed by the Cartesian net and a family of circles, and also by the Cartesian net and a family of second-order curves. Bibliography: 4 titles.
About the authors
Aleksandr Mikhailovich Shelekhov
Moscow State Pedagogical University
Email: amshelekhov@rambler.ru
Doctor of physico-mathematical sciences, Professor
References
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- В. Бляшке, Введение в геометрию тканей, Физматлит, М., 1959, 144 с.
- В. Б. Лазарева, А. М. Шелехов, “О триангуляциях плоскости пучками коник”, Матем. сб., 198:11 (2007), 107–134
- М. А. Половцева, “О некоторых детерминантных многообразиях в $mathbb{P}^5$ и $mathbb{P}^9$ как образах алгебраических систем плоских кривых второй и третьей степени”, Конструктивная алгебраическая геометрия, Респ. сб. науч. тр., 190, Ярославский пед. ин-т, Ярославль, 1980, 100–114
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