Flux Surfaces According to Killing Magnetic Vectors in Riemannian Space $\mathbb{S}ol3$

Year 2023, Volume: 6 Issue: 2, 89 - 100, 30.06.2023

Nourelhouda Benmensour , Fouzi Hathout

https://doi.org/10.33401/fujma.1163741

Abstract

In this paper, we define flux surface as surfaces in which its normal vector is orthogonal to the vector corresponding to a flux with its associate scalar flux functions in ambient manifold M. Next, we determine, in 3-dimensional homogenous Riemannian manifold $\mathbb{S}ol3$, the parametric flux surfaces according to the flux corresponding to the Killing magnetic vectors and we calculate its associate scalar flux functions. Finally, examples of such surfaces are presented with their graphical representation in Euclidean space.

Keywords

Flux, Flux surface, Killing magnetic, Scalar flux function, $\mathbb{S}ol3$ manifold

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