Ohnita's conjecture on minimal two-spheres in quaternionic projective space

Let $f:S^2\to\textbf{HP}^n$ be a proper minimal immersion, meaning that $f(S^2)$ is not contained in any totally geodesic submanifold of $\textbf{HP}^n$, and suppose that $f$ has constant curvature. The immersions $f_\lambda$, $f_{\lambda,m,t}$, $f_{m_1,m_2}$, and $f'_{m_1,m_2}$ are the families of minimal constant-curvature immersions constructed in the paper, with $\lambda\in\{1,3,\ldots,2n+1\}$. Ohnita's conjecture. The immersion $f$ is congruent to one of $f_\lambda$, $f_{\lambda,m,t}$, $f_{m_1,m_2}$, or $f'_{m_1,m_2}$. This extends Ohnita's proposed classification of proper minimal constant-curvature two-spheres in quaternionic projective space; the paper proves the listed homogeneous families and their noncongruence properties, while the asserted completeness of the classification remains open.