Generic singularities of spherical orthotomic curves associated with spherical pedal curves

TL;DR

This paper classifies the singularities of spherical orthotomic curves related to spherical pedal curves in n-dimensional spheres, providing a comprehensive understanding of their geometric properties.

Contribution

It introduces the concept of spherical orthotomic curves relative to a point and classifies their singularities, extending the theory of spherical pedal curves.

Findings

Classified singularities of spherical orthotomic curves

Established relationships between pedal and orthotomic curves in spheres

Provided a framework for analyzing singularities in higher dimensions

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.