Bolton, J. and Vrancken, L. (2009) 'Transforms for minimal surfaces in the 5-sphere.', Differential geometry and its applications., 27 (1). pp. 34-46.
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.
|Keywords:||Sphere, Minimal surface, Ellipse of curvature, Lagrangian submanifold, Complex projective space.|
|Full text:||PDF - Accepted Version (198Kb)|
|Publisher Web site:||http://dx.doi.org/10.1016/j.difgeo.2008.06.005|
|Record Created:||15 Feb 2008|
|Last Modified:||21 Oct 2010 15:01|
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