Some integral curves according to quasi-frame in Euclidean 3-space
Year: 2025
Type: article
Abstract: This study explores integral curves associated with the quasi-frame in three-dimensional Euclidean space . We focus specifically on the quasi-normal and quasi-binormal vectors. We derive the Frenet apparatus for these integral curves based on the quasi-frame elements. Our analysis reveals significant relationships between the integral curves and the original curve’s Frenet frame. We present explicit expressions for the Frenet–Serret apparatus of both quasi-normal and quasi-binormal curves. Moreover, we identify conditions under which these integral curves qualify as general helices or Salkowski curves. The study examines geometric relationships, including involute-evolute pairs and Bertrand pairs. Additionally, we analyze conditions that prevent the formation of Mannheim curve pairs.
Source: Scientific African
Authors: Ayman Elsharkawy, Hasnaa Baizeed
Institutions: Tanta University, Beni-Suef University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $590
OpenAlex ID: W4407463711