Abstract
The aim of this paper is to study AW(k)-type (1 ≤ k ≤ 3) curves according to the equiform differential geometry of the pseudo-Galilean space G1 3. We give some geometric properties of AW(k) and weak AW(k)-type curves. Moreover, we give some relations between the equiform curvatures of these curves. Finally, examples of some special curves are given and plotted to support our main results.
Highlights
The geometry of space is associated with mathematical group
The aim of this paper is to study AW(k)-type (1 ≤ k ≤ 3) curves according to the equiform differential geometry of the pseudo-Galilean space G13
This section contains some important facts about equiform geometry
Summary
The geometry of space is associated with mathematical group. The idea of invariance of geometry under transformation group may imply that, on some spacetimes of maximum symmetry there should be a principle of relativity which requires the invariance of physical laws without gravity under transformations among inertial systems [1]. The theory of curves and the curves of constant curvature in the equiform differential geometry of the isotropic spaces I31 , I32 and the Galilean space G3 are described in [2] and [3], respectively. The pseudo-Galilean space is one of the real Cayley-Klein spaces. AW(k)-type curves; spacelike and timelike curves; general helix; equiform geometry; pseudo-Galilean space. In 3-dimensional Galilean space and Lorentz space, the curves of AW(k)-type were investigated in [6, 8].
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