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http://dx.doi.org/10.5831/HMJ.2022.44.3.391

ON CHARACTERIZATIONS OF SPHERICAL CURVES USING FRENET LIKE CURVE FRAME  

Eren, Kemal (Department of Mathematics, Sakarya University)
Ayvaci, Kebire Hilal (Department of Mathematics, Ordu University)
Senyurt, Suleyman (Department of Mathematics, Ordu University)
Publication Information
Honam Mathematical Journal / v.44, no.3, 2022 , pp. 391-401 More about this Journal
Abstract
In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.
Keywords
Flc frame; polynomial curve; spherical curve; the axis of curvature; osculating sphere;
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