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

الأصل · EN

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+Kⁿ=1 for the Gauss curvature K and the normal curvature Kⁿ 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.