Local rigidity of minimal surfaces in a hyperquadric Q2

In this paper, we study rigidity of a minimal immersion f from a surface M into a hyperquadric Q2. It is proved that except a case that f is totally geodesic, totally real with Gauss curvature K=0, then up to a rigidity, f is uniquely determined by the first fundamental form, the second fundamental form and Kähler angle.