Abstract. We report our recent result (joint work with R. Aiyama, K. Akutagawa and M. Umehara) on a global correpondence between CMC surfaces in $P^3(c^2)$ or in $S^3(c^2)$ and a pair of non-conformal harmonic maps into $S^2$ in a same associated family.
AMSclassification. Primary 53C42, 53A10; Secondary 58E20
Keywords. CMC surface, Gauss map