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:||(AM) Accepted Manuscript|
Download PDF (198Kb)
|Publisher Web site:||http://dx.doi.org/10.1016/j.difgeo.2008.06.005|
|Date accepted:||No date available|
|Date deposited:||15 February 2008|
|Date of first online publication:||28 October 2007|
|Date first made open access:||No date available|
Save or Share this output
|Look up in GoogleScholar|