In this paper, we define a new kind of curve called $N$-slant curve whose principal normal vector field makes a constant angle with the Reeb vector field $\xi$ in Sasakian $3$-manifolds. Then, we give some characterizations of $N$-slant curves in Sasakian $3$-manifolds and we obtain some properties of the curves in $\mathbb{R}^{3}(-3)$. Moreover, we investigate the conditions of $C$-parallel and $C$-proper mean curvature vector fields along $N$-slant curves in Sasakian $3$-manifolds. Finally, we study $N$-slant curves of type $AW(k)$ where k=1,2 or 3.
Primary Language | English |
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Subjects | Algebraic and Differential Geometry |
Journal Section | Research Article |
Authors | |
Early Pub Date | April 17, 2024 |
Publication Date | April 23, 2024 |
Submission Date | November 29, 2023 |
Acceptance Date | January 25, 2024 |
Published in Issue | Year 2024 Volume: 17 Issue: 1 |