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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 2, Pages 76–87
(Mi ivm9210)
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This article is cited in 1 scientific paper (total in 1 paper)
Canonical frame of a curve on a conformal plane
A. M. Shelekhov Tver State University,
33 Zhelyabov str., Tver, 170100 Russia
Abstract:
It is shown how one can investigate a differential geometry of smooth curve on conformal plane by the Elie Cartan method of exterior forms and moving frame. We find the canonical form of the derivation equations of a curve (the latter not being a circle) in case of semi-isotropic frame. We give a new proof of the theorem that the constant (specifically, zero) conformal curvature curves are the rhumb line. We integrate a system of structure equations of the isotropy subgroup of a point.
Keywords:
Elie Cartan method of exterior forms and moving frame, conformal geometry, conformal curvature of a curve, isotropy subgroup, canonical equations of a plane curve.
Received: 21.07.2015
Citation:
A. M. Shelekhov, “Canonical frame of a curve on a conformal plane”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 2, 76–87; Russian Math. (Iz. VUZ), 61:2 (2017), 64–73
Linking options:
https://www.mathnet.ru/eng/ivm9210 https://www.mathnet.ru/eng/ivm/y2017/i2/p76
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Abstract page: | 163 | Full-text PDF : | 61 | References: | 31 | First page: | 10 |
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