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

Articles

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.

Keywords

minimal surface normal curvature Gauss curvature pinching 

MSC(2010)

53C42 53A10 

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Notes

Acknowledgements

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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsLiaoning UniversityShenyangChina

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