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

作者：Yang, Dan^*

来源：Science China Mathematics, 2019, 62(9): 1779-1792.

DOI：10.1007/s11425-017-9220-0

• minimal surface
• normal curvature
• Gauss curvature
• pinching

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.

• 出版日期2019-9
• 单位辽宁大学