Pedal-Contrapedal curve pairs of spacelike frontals in null sphere

Abstract

Due to the curves that exhibiting singularities in the null sphere can not be studied directly. Hence we aim to analyze these problems by using the duality theory. In addition, we define the pedal curves and contrapedal curves of spacelike frontals and investigate their geometric properties in null sphere. We also consider sufficient singular conditions for the contrapedal curves. Moreover, we give the particularrelations between pedal-contrapedal curve pairs and Involute-evolute curve pairs.