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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 2, Pages 76–87 (Mi ivm9210)  

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
Full-text PDF (195 kB) Citations (1)
References:
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
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 2, Pages 64–73
DOI: https://doi.org/10.3103/S1066369X17020086
Bibliographic databases:
Document Type: Article
UDC: 514.756
Language: Russian
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
Citation in format AMSBIB
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\pages 76--87
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\issue 2
\pages 64--73
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  • https://www.mathnet.ru/eng/ivm/y2017/i2/p76
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:31
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