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Title: Applications of Quaternionic Holomorphic Geometry to minimal surfaces
Authors: Leschke, K.
Moriya, K.
First Published: 16-Nov-2016
Publisher: De Gruyter Open
Citation: Complex Manifolds, 2016, 3 (1)
Abstract: 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.
DOI Link: 10.1515/coma-2016-0015
eISSN: 2300-7443
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: © 2016 K. Leschke and K. Moriya. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)
Appears in Collections:Published Articles, Dept. of Mathematics

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