On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2-space

In this paper, we mainly investigate (contra)pedals and (anti)orthotomics of frontals in the de Sitter 2-space from the viewpoint of singularity theory and differential geometry. We utilize the de Sitter Legendrian Frenet frames to provide parametric representations of (contra)pedal curves of spacelike and timelike frontals in the de Sitter 2-space and to investigate the geometric and singularity properties of these (contra)pedal curves. We then introduce orthotomics of frontals in the de Sitter 2-space and explain these orthotomics as wavefronts from the viewpoint of Legendrian singularity theory. Furthermore, we generalize these methods to study antiorthotomics of frontals in the de Sitter 2-space.