Publication details for Dr John BoltonBolton, John. & Vrancken, Luc. (2009). Transforms for minimal surfaces in the 5-sphere. Differential Geometry and its Applications 27(1): 34-46
- Publication type: Journal Article
- ISSN/ISBN: 0926-2245
- DOI: 10.1016/j.difgeo.2008.06.005
- Keywords: Sphere; Minimal surface; Ellipse of curvature; Lagrangian submanifold; Complex projective space
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associate to such a surface a corresponding ruled minimal Lagrangian submanifold of complex projective 3-space, which gives the converse of a construction considered in a previous paper, and illustrate this explicitly in the case of bipolar minimal surfaces.
This paper is posted on the Durham eprints server. Acceptance in `Differential Geometry and its Applications' is expected soon.