[Complex Manifolds] Applications of Quaternionic HolomorphicGeometry to minimal surfaces.pdf (1.33 MB)
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Applications of Quaternionic Holomorphic Geometry to minimal surfaces

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journal contribution
posted on 12.05.2017, 15:29 by K. Leschke, K. Moriya
In 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 Mathematics

Version

VoR (Version of Record)

Published in

Complex Manifolds

Publisher

De Gruyter Open

eissn

2300-7443

Acceptance date

13/10/2016

Copyright date

2016

Available date

12/05/2017

Publisher version

https://www.degruyter.com/view/j/coma.2016.3.issue-1/coma-2016-0015/coma-2016-0015.xml

Language

en

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