# On Slant Magnetic Curves in $S$-manifolds

## TL;DR

This paper characterizes slant normal magnetic curves in $S$-manifolds, identifying specific types such as geodesics, circles, and helices, and provides explicit constructions and equations for these curves.

## Contribution

It provides a complete classification of slant normal magnetic curves in $S$-manifolds and explicit parametric equations for these curves.

## Key findings

- Classification of slant normal magnetic curves as geodesics, circles, and helices.
- Explicit parametric equations for slant magnetic curves in $ ext{R}^{2n+s}(-3s)$.
- Conditions under which curves are slant normal magnetic 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.