Abstract
In curve theory, Mannheim curves are well-established objects that have been extensively analyzed in both Euclidean and Minkowski 3-space. A curve $\varphi $ is classified as a Mannheim curve if there exists a corresponding relationship with another space curve $\varphi ^{\star }$ such that, at corresponding points on each curve, the principal normal lines of $\varphi $ align with the binormal lines of $\varphi ^{\star }$. In this study, we focus on examining the differential geometric properties of spacelike Mannheim curves within Minkowski 3-space, utilizing a novel approach. Through this method, we derive the conditions under which a spacelike curve qualifies as a Mannheim curve and introduce new examples of Mannheim curves that are not covered in the classical framework.
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Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Submission Date | August 28, 2025 |
| Acceptance Date | October 17, 2025 |
| Publication Date | February 23, 2026 |
| DOI | https://doi.org/10.47000/tjmcs.1773037 |
| IZ | https://izlik.org/JA56RX37XY |
| Published in Issue | Year 2026 Volume: 18 Issue: 1 |