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 $S^n$, 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.