Evolutes of Fronts in de Sitter and Hyperbolic Spheres

Abstract

The evolute of a regular curve is a classical object from the viewpoint of differential geometry. We study some types of curves such as framed curves, framed immersion curves, frontal curves and front curves in 2-dimensional de Sitter and hyperbolic spaces. Also, we investigate the evolutes and some of their properties of fronts at singular points under some conditions. Finally, some computational examples in support of our main results are given and plotted.

Spacelike curves and evolution equations in de Sitter 3-space

“…In future works, we plan to study the geometry of moving spacelike and timelike curves in different spaces like Galilean and pseudo-Galilean spaces for different queries and further improve the results in this paper, combined with the techniques and results in [18][19][20][21].…”