Hyperbolic Lawson Surface $r=2$
The analogue, in ${\mathbb H}^3 \subset {\mathbb R}^{1,3} \subset {\mathbb R}^{1,4}$,
of Lawson's minimal tori/Klein bottles are given by:
$$f(u, v) = \left(\cosh v \cosh u, \,
\cosh v \sinh u, \, \sinh v \cos ru, \, \sinh v \sin ru \right).$$
They are minimal surfaces in ${\mathbb H}^3$ invariant under an $SO(1,1) \times SO(2)$ action.
The surface shown here is the same surface in ${\mathbb R}^{1,4}$ under a projection
to a different ${\mathbb H}^3$. It is Moebius equivalent but not itself minimal.
The conformal parameterization used to compute this surface is different from the displayed equations,
which only produce half of the surface.
This surface is foliated by circles.
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