Bulletin of the
Korean Mathematical Society BKMS

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