A construction of surfaces in spaces of constant curvature via integrable system method

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We defined complex constant mean curvature surfaces by a natural generalization of constant mean curvature surfaces in Euclidean three space and classified real form surfaces, such as constant mean curvature or constant Gauss curvature surfaces in spaces of constant curvature, for a complex constant mean curvature surface. We also characterized equivariant harmonic maps in complex projective spaces via potentials, which are matrix valued 1-forms. Moreover, a construction method of equivariant harmonic maps in complex projective spaces has been obtained from the potentials.