Transforms for minimal surfaces in the 5-sphere

Bolton, John; Vrancken, Luc

doi:10.1016/j.difgeo.2008.06.005

Transforms for minimal surfaces in the 5-sphere

Bolton, John; Vrancken, Luc

Authors

Dr John Bolton john.bolton@durham.ac.uk
Bank Teacher

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.