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 -manifold $(M^{2m+s},\phi ,{\xi }_{\alpha },{\eta }^{\alpha },g)$ if and only if it belongs to a list of slant $\phi$-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.

16 pages