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Explicit Examples of Motions of Inextensible Curves in Spherical Space S3 |
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PP: 77-83 |
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Author(s) |
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Samah Gaber Mohamed,
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Abstract |
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| In this paper we study the motion of curves in $3$-dimensional spherical
space $\mathbb{S}^{3}$. We derive the evolution equations of the orthonormal
frame and evolution equations for curvatures. Moreover, we give some
explicit examples of motions of inextensible curves in $\mathbb{S}^{3}$ and we
determine the curves from their intrinsic equations (curvature and torsion). Then we determine the surfaces that are generated by the motion of these
curves. To visualize these surfaces in
$\mathbb{S}^{3}$, we use the stereographic projection in $\mathbb{R}^{4}$.
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