Conformal minimal immersions of S 2 into $\mathbb{H}$ P 4

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 $\mathbb{C} $ P2n+1, which was projected into constant curvature conformal minimal two-spheres by twistor map π: $\mathbb{C} $ P2n+1→ $\mathbb{H}$ Pn. They calculated the case n=2. In this work, we deal with the case n=4 and a related geometry phenomenon.