Year: 2025
Type: article
Abstract: This paper explores Tzitzeica curves in three-dimensional Euclidean space through the use of modified orthogonal frames constructed via curvature and torsion functions. First, the fundamental differences between the classical Frenet frame and the modified orthogonal frame are clarified. Following this, the necessary and sufficient conditions under which a curve can be classified as a Tzitzeica curve relative to the modified frame are established. The study also presents characterization theorems for spherical Tzitzeica curves and Tz-general helices, supported by differential geometric expressions involving curvature and torsion functions. Furthermore, special cases such as anti-Salkowski curves and rectifying curves are examined.
Source: Cumhuriyet Science Journal
DOI: 10.17776/csj.1751734
Author: Esra Damar
Institution: Hitit Üniversitesi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414622935