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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.

Abstract

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.
Full text:PDF - Accepted Version (198Kb)
Status:Peer-reviewed
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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