Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON CHARACTERIZATIONS OF SPHERICAL CURVES USING FRENET LIKE CURVE FRAME

  • Received : 2022.03.02
  • Accepted : 2022.07.26
  • Published : 2022.09.01
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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.

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References

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