Conformal minimal surfaces immersed into

In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in by the twistor map . The construction is due to Eells and Wood's conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in . Under this characterization, we construct eight families of conformal minimal surfaces in . Then, we study horizontal Veronese sequences in and , and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in with constant curvature and .