Rigidity of Beltrami fields with a non-constant proportionality factor

TL;DR

This paper proves that bounded Beltrami fields with a variable proportionality factor depending on two variables exhibit symmetry if certain geometric conditions on the level sets are met.

Contribution

It establishes symmetry results for bounded Beltrami fields with non-constant proportionality factors under specific geometric conditions.

Findings

Bounded Beltrami fields are symmetric under certain conditions.

Symmetry holds if the proportionality factor depends on two variables.

Regular level sets being cylindrical or toroidal are key to the results.

Abstract

We prove that bounded Beltrami fields must be symmetric if a proportionality factor depends on 2 variables in the cylindrical coordinate and admits a regular level set diffeomorphic to a cylinder or a torus.