Abstract
AbstractIn 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.
Reference21 articles.
1. The conformal Gauss map of submanifolds of the Moebius space Global Anal No pages;Rigoli;Geom,1987
2. Dressing orbits of harmonic maps Duke Math No pages;Burstall;Journ,1995
3. On surfaces of stationary area bounded by two circels , or convex curves , in parallel planes No pages;Shiffman;Ann Math,1956
4. Harmonic maps into Lie groups ( classical solutions of the chiral model ) pages;Uhlenbeck;Geom,1989
5. Computer graphics tools for the study of minimal surfaces Communications of the pages;Callahan;ACM,1988
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献