Minimal Surfaces in A Complex Hyperquadric Q_n with Constant Kahler Angle

We consider a minimal immersion f: M\rightarrow Q_n from a surface M into a complex hyperquadric Q_n with constant Kahler angle, and the length of its second fundamental form is denoted by |B|. We obtain pinching results about |B|^2 when f is holomorphic and totally real, and characterize all the minimal compact surfaces without boundary when equality holds in the pinching results. Finally, we determine all the totally real minimal S^2 in Q_n satisfying a pinching condition.