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

Dan Yang

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arXiv · 1712.08486

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

Dan Yang

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Abstract

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.

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Dan Yang. 2017-12-22. Minimal surfaces in a unit sphere pinched by intrinsic curvature and normal curvature. https://arxiv.org/abs/1712.08486

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