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.
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