Beltrami vector fields with an icosahedral symmetry

Abstract

A vector field is called a Beltrami vector field, if $B\times (\nabla \times B)=0$. In this paper we construct two unique Beltrami vector fields $\mathfrak{I}$ and $\mathfrak{Y}$, such that $\nabla \times \mathfrak{I}=\mathfrak{I}$, $\nabla \times \mathfrak{Y}=\mathfrak{Y}$, and such that both have an orientation-preserving icosahedral symmetry. Both of them have an additional symmetry with respect to a non-trivial automorphism of the number field $\mathbb{Q}(\sqrt{5})$.

22 pages, 9 figures

References in corpus (2)

• Tight Beltrami fields with symmetry
• Trkalian fields: ray transforms and mini-twistors