Shoichi Fujimori, Shimpei Kobayashi, Wayne Rossman
Published 2006-02-25, updated 2009-12-25Version 2
This is an elementary introduction to a method for studying harmonic maps into symmetric spaces, and in particular for studying constant mean curvature (CMC) surfaces, that was developed by J. Dorfmeister, F. Pedit and H. Wu. There already exist a number of other introductions to this method, but all of them require a higher degree of mathematical sophistication from the reader than is needed here. The authors' goal was to create an exposition that would be readily accessible to a beginning graduate student, and even to a highly motivated undergraduate student. Constant mean curvature surfaces in Euclidean 3-space, and also spherical 3-space and hyperbolic 3-space, are described, along with the Lax pair equations that determine their frames. The simplest examples, including Delaunay surfaces and Smyth surfaces, are described in detail.
Comments: This is an introductory exposition on constructing constant mean curvature surfaces by techniques of integrable systems. A version with higher quality graphics exists at the home page of the Rokko Lectures in Mathematics series. Version 2: six minor errors repaired, and one figure repaired
Journal: Rokko Lectures in Mathematics 17, October 2005
Holomorphic Representation of Constant Mean Curvature Surfaces in Minkowski Space: Consequences of Non-Compactness in Loop Group Methods
Constant mean curvature surfaces with two ends in hyperbolic space
On the genus and area of constant mean curvature surfaces with bounded index
![QR code for arXiv:math/0602570 [math.DG]](http://oss.arxitics.com/images/favicon.svg)