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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（9）
• 页码范围: 1779-1792
• 页数: 14页
• 语种: 英文

摘要

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.