Non-rotational SO(4)-equivariant Willmore surfaces
These Willmore surfaces in the 3-sphere are each invariant under a 1-parameter subgroup of
$SO(4)$. Such a subgroup acts by $(z,w) \mapsto (e^{it}z, e^{r it}w)$, where $r$ is real.
The case $r=0$ is surfaces of revolution (not shown here).
The images are stereographic projections to ${\mathbb R}^3$, and therefore
also Willmore surfaces in ${\mathbb R}^3$.
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