调和映照与常平均曲率的曲面

The Surfaces with Constant Mean Curvature and Harmonic Maps

中文关键词:  常平均曲率的曲面  高斯映照  调和映照  Sinh－Laplace方程  Sinh－Gordon方程

英文关键词:Sinh Laplace equation  Sinh Gordon equation.

中文摘要:

      本文利用三维欧氏空间Ｒ^３或三维Ｍｉｎｋｏｗｓｋｉ空间Ｒ^2.1中常平均曲率的曲面与Ｓｉｎｈ－Ｌａｐｌａｃｅ方程和Ｓｉｎｈ－Ｇｏｒｄｏｎ方程之间的关系，研究了常平均曲率的曲面与Ｒ²到Ｓ²（或Ｈ²）及Ｒ^1.1到Ｓ^1.1（＋１）的调和映照之间的内在联系，并且提供了一种构造到球面Ｓ²，Ｈ²和Ｓ^1.1

英文摘要:

      In this paper, we study the intimate relations between the surfaces of constant mean curvature and the harmonic maps to S²,H² and S^1.1(+1) by using the relations between the surfaces of constant mean curvature in Euclidean space R^３ or Minkowski space R^2.1 and Sinh Laplace as well as Sinh Gordon equations. We also offer a method for constructing the harmonic maps to S²,H² and S^1.1(+1).