Frenet curve, associated curve, direction curve, donor curve, helix,

In this study, we introduce mappings that transform helices in Euclidean $ n $-space to non-null helices in Minkowski $ n $-space or Minkowski $ (n+1) $-space. Furthermore, we show that these mappings preserve the axes of the helices, and we also obtain the invariants of the mappings. Especially, by using these mappings, we give some examples of non-null helices which are constructed in Minkowski 3-space or Minkowski 4-space from some helices in Euclidean 3-space.

In this paper, we define a spacelike ac-slant curve whose scalar product of its acceleration vector and a unit non-null fixed direction is a constant in Minkowski 3-space. Furthermore, we give a characterization depending on the curvatures of the spacelike ac-slant curve. After that, we get the relationship between a spacelike ac-slant curve and several distinct types of curves, such as spacelike Lorentzian spherical curves, spacelike helices, spacelike slant helices, and spacelike Salkowski curves, enhancing our understanding of its geometric properties in Minkowski 3-space. Finally, we used Mathematica, a symbolic computation software, to support the notions of an ac-slant curve with attractive images.

In this article, we investigate polynomial helices in the n-dimensional semi-Euclidean space with index two for n ≥ 4. We obtain some families of spacelike and timelike polynomial helices. These helices have spacelike or timelike or null axes. After that, we give some examples of the spacelike and the timelike polynomial helices in the n-dimensional semi-Euclidean space with index two for n = 4,5 and 6.

In this work, we introduced the concept of a timelike acceleration-slant curve in three-dimensional Minkowski space, characterized by the property that the scalar product of a fixed unit direction and its acceleration vector remained constant. Moreover, we provided a classification of timelike acceleration-slant curves with a non-null axis based on their curvature properties. Later on, we explored the relationships between timelike acceleration-slant curves and various notable curves, including timelike helices, timelike slant helices, timelike Lorentzian spherical curve, and timelike Salkowski curves. To further illustrate and validate the theoretical results, we utilized Mathematica to generate visual representations.