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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 10, Pages 79–93
(Mi ivm9407)
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This article is cited in 4 scientific papers (total in 4 papers)
On hexagonal three-webs formed by Cartesian net and a family of circles
A. M. Shelekhov Tver State University,
33 Zhelyabov str., Tver, 170100 Russia
Abstract:
By the Elie Cartan's method we prove that there are only two types of regular three-webs formed by the Cartesian net and a family of circles: three-webs $(C_1)$, in which the family is formed by concentric circles, and the three-webs $(C_2)$, where all circles of the family have the same radius, and their centers lie on a line.
Keywords:
curvilinear three–web, regular three-web, circle three–web, three-web curvature.
Received: 23.10.2017
Citation:
A. M. Shelekhov, “On hexagonal three-webs formed by Cartesian net and a family of circles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 10, 79–93; Russian Math. (Iz. VUZ), 62:10 (2018), 68–81
Linking options:
https://www.mathnet.ru/eng/ivm9407 https://www.mathnet.ru/eng/ivm/y2018/i10/p79
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Abstract page: | 160 | Full-text PDF : | 44 | References: | 21 | First page: | 3 |
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