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Similar and self-similar curves in Minkowski \(n\)-space. (English) Zbl 1332.53018
Summary: In this paper, we investigate the similarity transformations in the Minkowski \(n\)-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of \(\mathbb E_1^n\). We determine the parametrizations of non-null self-similar curves in \(\mathbb E_1^n\).

MSC:
53A35 Non-Euclidean differential geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B25 Local submanifolds
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