Locally Isometric Families of Minimal Surfaces

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider a surface $M$ immersed in $\mathbb{R}^3$ with induced metric $g=ψδ_2$ where $δ_2$ is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain $M$ to lift to a minimal surface via the Weierstrauss-Enneper representation demanding the metric is of the above form. It is concluded that the associated surfaces connecting the prescribed minimal surface and its conjugate surface satisfy the system. Moreover, we find a non-trivial symmetry of the PDE which generates a one parameter family of surfaces isometric to a specified minimal surface. We demonstrate an instance of the analysis for the helicoid and catenoid.
7 pages, 2 figures

Keywords

Differential Geometry, Complex Variables, Primary 53A10; Secondary 30C55

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/128940

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609654
 http://arxiv.org/abs/math/0609654

Collections

arXiv