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Some results on p-shape curvatures of non-lightlike space curves. (English) Zbl 1409.53016
Summary: In this paper, we obtain some findings for a non-null curve parameterized by spherical arc length. We investigate the relationship between a non-null curve with \(p\)-shape curvatures and pseudospherical curves on \(S^2_1\) and \(H^2(-1)\). We introduce the concept of similar helix in Minkowski 3-space \(\mathbb E_1^3\). Besides, we explicitly determine the parametrizations of all non-lightlike self-similar curves by using the pseudo-spherical curves in \(\mathbb E_1^3\).
53A35 Non-Euclidean differential geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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