A New Approach on Curves of Constant Precession

TL;DR

This paper explores the properties of curves with constant precession, demonstrating they are a type of slant helix, and provides characterizations of these curves based on their spherical images.

Contribution

It introduces a new perspective by linking curves of constant precession to slant helices and generalizes the concept of slant helices through spherical image analysis.

Findings

Curves of constant precession are shown to be slant helices.

Spherical images of these curves are spherical slant helices.

Characterizations of slant helices are provided based on their spherical indicatrices.

Abstract

In this paper, we investigate a curve whose spherical image the tangent indicatrix and binormal indicatrix is slant helix and called it as a slant helix. We obtain that the spherical images are spherical slant helices defined by [3]. This notation is a generalization of a slant helix. Furthermore, we have given some characterizations for the slant helix and we show that a curve of constant precession is a slant helix.