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.
minimal surface normal curvature Gauss curvature pinching
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This work was supported by Chern Institute of Mathematics. The author thanks the referees for their professional suggestions about this paper which led to various improvements.
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