Work

Position Vectors of Curves in Isotropic Space $I^3$ and Their Relation to the Frenet Frame

Year: 2024

Type: article

Abstract: This paper investigates position vectors of arbitrary curves in isotropic 3-space (denoted by I^3). We first establish the relationship between a curve’s position vector and the Frenet frame. Then, we derive a natural representation of any curve’s position vector using curvature and torsion. Furthermore, we define various curves within isotropic space, including straight lines, plane curves, helices, general helices, Salkowski curves, and anti-Salkowski curves. Finally, graphical illustrations accompany illustrative examples to elucidate the discussed concepts.

Source: Turkish Journal of Mathematics and Computer Science

DOI: 10.47000/tjmcs.1488986

Authors: Tevfik Şahin, Gülnur Özyurt

Institution: Amasya Üniversitesi

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu

Award: G3977822894