On conformal minimal immersions with constant curvature from two-spheres into the complex hyperquadrics

In this paper, firstly we study the geometry of conformal minimal two-spheres immersed in the complex hyperquadric Qn−2Qn−2. Then we classify the linearly full irreducible conformal minimal immersions with constant curvature from S2S2 to Qn−2Qn−2 (n⩾7n⩾7) of isotropy order r=n−6r=n−6 under some conditions, which shows that all such immersions can be expressed by Veronese surfaces in CPn−1CPn−1 only under some conditions.