All superconformal surfaces in \R^4 in terms of minimal surfaces

Simple item page
dc.creatorDajczer, Marcos
dc.creatorTojeiro, Ruy
dc.date2007-10-28
dc.date2007-10-30
dc.date.accessioned2026-07-07T08:39:09Z
dc.date.available2026-07-07T08:39:09Z
dc.descriptionWe give an explicit construction of any simply-connected superconformal surface $ϕ\colon M^2\to \R^4$ in Euclidean space in terms of a pair of conjugate minimal surfaces $g,h\colon M^2\to\R^4$. That $ϕ$ is superconformal means that its ellipse of curvature is a circle at any point. We characterize the pairs $(g,h)$ of conjugate minimal surfaces that give rise to images of holomorphic curves by an inversion in $\R^4$ and to images of superminimal surfaces in either a sphere $\Sf^4$ or a hyperbolic space $\Hy^4$ by an stereographic projection. We also determine the relation between the pairs $(g,h)$ of conjugate minimal surfaces associated to a superconformal surface and its image by an inversion. In particular, this yields a new transformation for minimal surfaces in $\R^4$.
dc.identifierhttps://arxiv.org/abs/0710.5317
dc.identifierhttp://arxiv.org/abs/0710.5317
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140976
dc.subjectDifferential Geometry
dc.subject53B25
dc.titleAll superconformal surfaces in \R^4 in terms of minimal surfaces
dc.typetext

Files

Collections

arXiv