关键词: 极小二球, 高斯曲率, Veronese序列, 四元数射影空间

Abstract: This work is a generalization of Chen and Jiao's work, where they considered the question of explicit construction of some conformal minimal two-spheres of constant curvature in quaternionic projective space. The crucial point was to find some horizontal immersions derived from Veronese sequence in CP²ⁿ⁺¹, which was projected into constant curvature conformal minimal two-spheres by twistor map π:CP²ⁿ⁺¹→HPⁿ. They calculated the case n=2. In this work, we deal with the case n=4 and a related geometry phenomenon.

Key words: minimal two-sphere, Gaussian curvature, Veronese sequence, quaternionic projective space