Loop Group Methods for Constant Mean Curvature Surfaces
Loop Group Methods for Constant Mean Curvature Surfaces
复制标题
DOI：
--
复制
发表时间：
2006-02
期刊：
影响因子：
--
通讯作者：
S. Fujimori;Shimpei Kobayashi;W. Rossman
中科院分区：
文献类型：
--
作者：
S. Fujimori;Shimpei Kobayashi;W. Rossman
这是对研究对称空间调和映射的方法的基本介绍，特别是研究常平均曲率 (CMC) 曲面的方法，该方法由 J. Dorfmeister、F. Pedit 和 H. Wu 开发。已经有许多对该方法的其他介绍，但所有这些都需要读者比这里需要的更高程度的数学复杂性。作者的目标是创建一个可供刚开始的研究生甚至积极主动的本科生轻松理解的阐述。描述了欧几里得 3 空间、球面 3 空间和双曲 3 空间中的恒定平均曲率曲面，以及确定其框架的 Lax 对方程。详细描述了最简单的示例，包括 Delaunay 曲面和 Smyth 曲面。
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.