Magnetic Curves in $C$-manifolds

TL;DR

This paper investigates the properties of normal magnetic curves within $C$-manifolds, characterizing their geometric nature and providing explicit parametrizations in Euclidean spaces with $C$-structure.

Contribution

It establishes that magnetic trajectories under contact magnetic fields are $ heta_{eta}$-slant curves with specific curvature functions and offers explicit parametrizations in Euclidean $C$-manifolds.

Findings

Magnetic trajectories are $ heta_{eta}$-slant curves with certain curvature functions.

Explicit parametrizations of normal magnetic curves in $ ext{R}^{2n+s}$ are provided.

Characterization of magnetic curves in $C$-manifolds under contact magnetic fields.

Abstract

In this paper, we study normal magnetic curves in $C$-manifolds. We prove that magnetic trajectories with respect to the contact magnetic fields are indeed $\theta_{\alpha }$-slant curves with certain curvature functions. Then, we give the parametrizations of normal magnetic curves in $\mathbb{R}^{2n+s}$ with its structures as a $C$-manifold.