[Complex Manifolds] Applications of Quaternionic HolomorphicGeometry to minimal surfaces.pdf (1.33 MB)
Applications of Quaternionic Holomorphic Geometry to minimal surfaces
journal contribution
posted on 2017-05-12, 15:29 authored by K. Leschke, K. MoriyaIn this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface.
Funding
Both authors supported by JSPS KAKENHI Grant-in-Aids for Scientific Research (C), Grant Number 25400063.
History
Citation
Complex Manifolds, 2016, 3 (1)Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- VoR (Version of Record)