  We investigate the relation between quadrics and their Christoffel duals on
the one hand, and certain zero mean curvature surfaces and their Gauss maps on
the other hand. To study the relation between timelike minimal surfaces and the
Christoffel duals of 1-sheeted hyperboloids we introduce para-holomorphic
elliptic functions. The curves of type change for real isothermic surfaces of
mixed causal type turn out to be aligned with the real curvature line net.
