We consider a surface M immersed in ℝ3 with induced metric g = φδ2 where δ2 is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain M to lift to a minimal surface via the Weierstrauss-Enneper representation, demanding the metric is of the above form. It is concluded that the associated surfaces connecting the prescribed minimal surface and its conjugate surface satisfy the system. Moreover, we find a non-trivial symmetry of the PDE which generates a one parameter family of surfaces isometric to a specified minimal surface.
|Original language||English (US)|
|Number of pages||6|
|Journal||Balkan Journal of Geometry and its Applications|
|State||Published - Jun 24 2008|
All Science Journal Classification (ASJC) codes
- Geometry and Topology