Minkowski minimal surfaces in \({\mathbb R}^3_1\) with minimal focal surfaces (Q839707)

In the Euclidean 3-space \(\mathbb{R}^3\) a focal surface \(\Psi\) of a minimal surface \(\Phi\) cannot be a minimal surface again. This is not true in the Lorentz 3-space \(\mathbb{R}^3_1\); here there are two one-parameter families of minimal surfaces with this property, namely a spacelike and a timelike one which may be explicitely determined by the author. Each such surface \(\Phi\) is the associate of a minimal surface of rotation with an isotropic axis. Finally the focal surfaces \(\Phi\) of our class of surfaces \(\Psi\) are classified.