Abstract: In this work, we construct six examples of conformal minimal two-spheres surfaces with constant curvatures of 4/7, 4/19, and 4/27 by the twistor map π:CP⁷→HP³. By the twistor map, we know that the horizontal minimal surfaces in CP²ⁿ⁺¹ are equivalent to the minimal surfaces in HPⁿ, and many conclusions about conformal minimal two-spheres with constant curvatures in CPⁿ have been given. Based on Bolton's conclusion and Chen's general method to construct conformal minimal two-spheres, we get some conformal minimal two-sphere surfaces in HP³.

Key words: quaternionic projective space, conformal minimal surface, twistor map