A New Representation for Slant Curves in Sasakian 3-Manifolds

Year 2024, , 277 - 289, 23.04.2024

Osman Ateş , İsmail Gök , Yusuf Yaylı

https://doi.org/10.36890/iejg.1397659

Abstract

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.

Keywords

Slant helices, Mean curvature vector fields, Curves of AW(k)-type, Sasakian manifolds

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