In this paper, we study the intimate relations between the surfaces of constant mean curvature and the harmonic maps to S2,H2 and S1.1(+1) by using the relations between the surfaces of constant mean curvature in Euclidean space R3 or Minkowski space R2.1 and Sinh Laplace as well as Sinh Gordon equations. We also offer a method for constructing the harmonic maps to S2,H2 and S1.1(+1). |