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Transforms for minimal surfaces in the 5-sphere.

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.

Item Type:Article
Keywords:Sphere, Minimal surface, Ellipse of curvature, Lagrangian submanifold, Complex projective space.
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Record Created:15 Feb 2008
Last Modified:21 Oct 2010 15:01

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