Geodesic
Canonical frame of a curve on a conformal plane
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 76-87

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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. 
@article{IVM_2017_2_a7,
     author = {A. M. Shelekhov},
     title = {Canonical frame of a curve on a conformal plane},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--87},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_2_a7/}
}
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A. M. Shelekhov. Canonical frame of a curve on a conformal plane. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 76-87. http://geodesic.mathdoc.fr/item/IVM_2017_2_a7/