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

TL;DR

This paper classifies all homogeneous two-spheres with constant curvature in quaternionic projective space, revealing more minimal examples than previously conjectured, thus advancing understanding of minimal submanifolds in this geometric setting.

Contribution

It provides a complete classification of homogeneous minimal two-spheres with constant curvature in quaternionic projective space, surpassing prior conjectures.

Findings

More minimal constant curved two-spheres in HP^n than previously conjectured

Complete classification of homogeneous two-spheres in quaternionic projective space

Enhanced understanding of minimal submanifolds in quaternionic geometry

Abstract

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