This article is cited 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.

UDC: 514.756

Received: 21.07.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:2, 64–73

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