Minimal surfaces in a unit sphere pinched by intrinsic curvature and normal curvature

We establish a nice orthonormal frame field on a closed surface minimally immersed in a unit sphere Sn, under which the shape operators take very simple forms. Using this frame field, we obtain an interesting property K + K~N= 1 for the Gauss curvature K and the normal curvature K~N if the Gauss curvature is positive. Moreover, using this property we obtain the pinching on the intrinsic curvature and normal curvature, the pinching on the normal curvature, respectively.