摘要
本文利用三维欧氏空间Ｒ３或三维Ｍｉｎｋｏｗｓｋｉ空间Ｒ２．１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Ｒ１．１到Ｓ１．１（＋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Ｓ１．
In this paper, we study the intimate relations between the surfaces of constant mean curvature and the harmonic maps to S 2,H 2 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 S 2,H 2 and S 1.1 (+1).
基金
国家自然科学基金
