Pedal curves of hyperbolic frontals and their singularities

The purpose of this paper is to introduce pedal curves of spacelike frontals in the hyperbolic 2-space and investigate the singularities of these hyperbolic pedal curves. We classify the singularities of hyperbolic pedal curves for non-singular and singular dual curve germs. To do this we make use of several important results from the Legendrian singularity theory. We explore how the curvatures of the original spacelike frontal and the location of the pedal point affect on the singularities of the corresponding pedal curve. More specifically, we show that for non-singular dual curve germs, the singularities of a pedal curve depend upon the singularities of the first hyperbolic Legendrian curvature germ and the location of the pedal point, whereas for singular dual curve germs, the singularities depend upon the singularities of both hyperbolic Legendrian curvature germs and also the location of the pedal point. Several examples with figures are provided to support our results.