Minimal two-spheres with constant curvature in the quaternionic projective space

Abstract

In this paper we completely classify the homogeneous two-spheres, especially, the minimal homogeneous ones in the quaternionic projective space ${\text{HP}}^n$. According to our classification, more minimal constant curved two-spheres in ${\text{HP}}^n$ are obtained than Ohnita conjectured in the paper "Homogeneous harmonic maps into projective space, Tokyo J Math, 1990, 13(1): 87-116".

This paper has been accepted for publication in SCIENCE CHINA Mathematics