Dr John Bolton john.bolton@durham.ac.uk
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Transforms for minimal surfaces in the 5-sphere
Bolton, John; Vrancken, Luc
Authors
Luc Vrancken
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.
Citation
Bolton, J., & Vrancken, L. (2009). Transforms for minimal surfaces in the 5-sphere. Differential Geometry and its Applications, 27(1), 34-46. https://doi.org/10.1016/j.difgeo.2008.06.005
Journal Article Type | Article |
---|---|
Online Publication Date | Oct 28, 2007 |
Publication Date | Feb 1, 2009 |
Deposit Date | Feb 15, 2008 |
Publicly Available Date | Feb 15, 2008 |
Journal | Differential Geometry and its Applications |
Print ISSN | 0926-2245 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 27 |
Issue | 1 |
Pages | 34-46 |
DOI | https://doi.org/10.1016/j.difgeo.2008.06.005 |
Keywords | Sphere, Minimal surface, Ellipse of curvature, Lagrangian submanifold, Complex projective space. |
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