On curves of constant torsion I

TL;DR

This paper presents an explicit method to construct closed curves with constant torsion and positive curvature, and explores their restrictions on convex surfaces.

Contribution

It provides a new explicit construction for such curves and analyzes their geometric constraints on convex surfaces.

Findings

Constructed explicit closed curves with constant torsion and positive curvature.

Identified restrictions on these curves when constrained to convex surfaces.

Enhanced understanding of the geometry of curves with constant torsion.

Abstract

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.