Hyperbolic Lawson Surface $r=5$
Stereographic projections to ${\mathbb R}^3$, from three different points,
of the same equivariant Willmore surface in ${\mathbb S}^3$. The projection from $(0,0,0,1)$
is the Poincare ball image of a minimal surface in ${\mathbb H}^3$,
$f(u,v) = \left(\cosh v \cosh u, \,
\cosh v \sinh u, \, \sinh v \cos 5 u, \, \sinh v \sin 5 u \right).$
The other two projections are Möbius equivalent, but not isometric. They are
all Willmore surfaces in ${\mathbb R}^3$, conformally equivariant with respect to
$SO(1,1) \times SO(2)$.
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