Rigidity of Conformal Minimal Immersions of Constant Curvature from $$S^2$$ to $$Q_4$$

Abstract

Geometry of conformal minimal two-spheres immersed in G(2, 6; R) is studied in this paper by harmonic maps. We construct a non-homogeneous constant curved minimal two-sphere in G(2, 6; R), and give a classification theorem of linearly full conformal minimal immersions of constant curvature from S 2 to G(2, 6; R), or equivalently, a complex hyperquadric Q 4 , which illustrates minimal two-spheres of constant curvature in Q 4 are in general not congruent.