Similar and self-similar curves in Minkowski $n$-space
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 2071-2093
https://doi.org/10.4134/BKMS.2015.52.6.2071
Published online November 30, 2015
Mustafa \"{O}zdemir and Hakan Simsek
Akdeniz University, Akdeniz University
Abstract : 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 $\mathbb{E}_{1}^{n}$.
Keywords : Lorentzian similarity geometry, similarity transformation, similarity invariants, similar curves, self-similar curves
MSC numbers : 53A35, 53A55, 53B30
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