On Slant Magnetic Curves in $S$-manifolds

Abstract

We consider slant normal magnetic curves in $(2n+1)$-dimensional $S$-manifolds. We prove that $\gamma $ is a slant normal magnetic curve in an $% S $-manifold $(M^{2m+s},\varphi ,\xi _{\alpha },\eta ^{\alpha },g)$ if and only if it belongs to a list of slant $\varphi $-curves satisfying some special curvature equations. This list consists of some specific geodesics, slant circles, Legendre and slant helices of order $3$. We construct slant normal magnetic curves in $\mathbb{R}^{2n+s}(-3s)$ and give the parametric equations of these curves.