Helicoidal minimal surfaces in \(\mathbb H^{2} \times \mathbb R\) (Q2907029)

Screw motions in \(\mathbb H^{2} \times \mathbb R\) are rigid motions generated by rotations in \(\mathbb H^2\) and vertical translations along \(\mathbb R\). A surface in \(\mathbb H^{2} \times \mathbb R\) is called \textit{helicoidal} it it is invariant under a \(1\)-parameter group of screw motions. The authors obtain a complete description of the minimal surfaces that are helicoidal. An important result is that conjugate surfaces of the parabolic and hyperbolic helicoids in \(\mathbb H^{2} \times \mathbb R\) are certain types of catenoids.