Generic singularities of spherical orthotomic curves associated with spherical pedal curves

Abstract

For the n-dimensional spherical pedal curve $ped_{\gamma,P}$ with respect to an n-dimensional spherical unit speed curve $\gamma$ and a given point $P \in S^n$, we define the spherical orthotomic curve of $\gamma$ relative to the point $P$, and classify singularities of spherical orthotomic curves.