On spacelike equiform-Bishop Smarandache curves on S12 $S_{1}^{2}$

Abstract

Abstract In this paper, we introduce the equiform-Bishop frame of a spacelike curve r lying fully on S12 $S_{1}^{2}$ in Minkowski 3-space ℝ13 $\mathbb {R}^{3}_{1}$. By using this frame, we investigate the equiform-Bishop Frenet invariants of special spacelike equiform-Bishop Smarandache curves of a spacelike base curve in ℝ13 $\mathbb {R}^{3}_{1}$. Furthermore, we study the geometric properties of these curves when the spacelike base curve r is specially contained in a plane. Finally, we give a computational example to illustrate these curves.

Keywords

• Smarandache curve
• Equiform Frenet frame
• Bishop frame
• Minkowski 3-space