Classification of conformal minimal immersions of constant curvature from $S^2$ to $Q_3$

Abstract

In this paper, we study geometry of conformal minimal two-spheres immersed in complex hyperquadric $Q_3$. We firstly use Bahy-El-Dien and Wood's results to obtain some characterizations of the harmonic sequences generated by conformal minimal immersions from $S^2$ to $G(2,5;\mathbb{R})$. Then we give a classification theorem of linearly full totally unramified conformal minimal immersions of constant curvature from $S^2$ to $G(2,5;\mathbb{R})$, or equivalently, a complex hyperquadric $Q_3$.