Research Article
Year 2025,
Volume: 46 Issue: 3, 595 - 600, 30.09.2025
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.
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There are 27 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2025 |
| Submission Date | July 26, 2025 |
| Acceptance Date | September 22, 2025 |
| Published in Issue | Year 2025 Volume: 46 Issue: 3 |
