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Binormal motions of inextensible curves in de-Sitter space \(\mathbb{S}^{2,1}\). (English) Zbl 1378.53016

Summary: In the present work, we continue our study of motions of inextensible curves in de-Sitter space \(\mathbb{S}^{2,1},\) that we started in [1]. The binormal motions of timelike curves and spacelike curves with a timelike normal vector in \(\mathbb{S}^{2,1}\) are described and studied. By the motions of these types of curves, new surfaces (we will call them Hasimoto surfaces) are constructed and plotted by using the hollow ball model by Mathematica 7.

MSC:

53A35 Non-Euclidean differential geometry
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53Z05 Applications of differential geometry to physics

Software:

Mathematica
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Full Text: DOI

References:

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