Affine dual curve pair under the equi-transform of affine framed curve

Abstract

In this paper, we define the affine pedal and contrapedal curve (collectively referred to as affine dual curve pair) under the equi-transform in $SL(2,R)$-system to solve the singularity problem. Then, we investigate the singular properties of affine dual curve pair under the equi-transform and give the classifications of singular points of affine dual curve pair. In addition, we bring the affine dual form to other affine curve pair like equi-affine evoulute-involute and study the new affine dual relationships.