It is shown that a minimal surface in ℍ 2× ℝ is invariant under a one-parameter group of screw motions if and only if it lies in the associate family of helicoids. It is also shown that the conjugate surfaces of the parabolic and hyperbolic helicoids in ℍ 2× ℝ are certain types of catenoids.
|Number of pages||15|
|Journal||Bulletin of the Australian Mathematical Society|
|Publication status||Published - 2012 Aug|
- associate minimal surfaces
- conjugate minimal surfaces
- helicoidal surface
ASJC Scopus subject areas