- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Pseudo-Hermitian magnetic curves in normal almost contact metric 3-manifolds Commun. Korean Math. Soc.Published online August 31, 2020 Ji-Eun Lee Chonnam National University Abstract : In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric $3$-manifold equipped with the canonical affine connection $\hat\nabla^t$ is a slant helix with pseudo-Hermitian curvature $\hat{\kappa}=\mid q\mid\sin\theta$ and pseudo-Hermitian torsion $\hat\tau=q\cos\theta$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric $3$-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve $\gamma$ in a quasi-Sasakian 3-manifold $M$ is a slant curve with curvature $\kappa=\mid (t-\alpha)\cos\theta\>+q\mid\sin\theta$ and torsion $\tau=\alpha+\{(t-\alpha)\cos\theta+q\}\cos\theta$. These curves are not helices, in general. Note that if the ambient space $M$ is a $\alpha$-Sasakian $3$-manifold then $\gamma$ is a slant helix. Keywords : magnetic curve, slant curve, almost contact metric 3-manifold, CR-structure MSC numbers : 53B25, 53C25 Full-Text :