Classification of conformal minimal immersions of constant curvature from S² to Q₃

Abstract

In this paper, we study geometry of conformal minimal two-spheres immersed in complex hyperquadric Q₃. We firstly use Bahy-El-Dien and Wood's results to obtain some characterizations of the harmonic sequences generated by conformal minimal immersions from S² to G(2,5;ℝ). Then we give a classification theorem of linearly full totally unramified conformal minimal immersions of constant curvature from S² to G(2,5;ℝ), or equivalently, a complex hyperquadric Q₃.