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The Riemannian geometry of superminimal surfaces in complex space forms

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Abstract

This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou University, 310028, Hangzhou, China

    Shen Yibing

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  1. Shen Yibing
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Supported by the National Natural Science Fundation of China.

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Yibing, S. The Riemannian geometry of superminimal surfaces in complex space forms. Acta Mathematica Sinica 12, 298–313 (1996). https://doi.org/10.1007/BF02106984

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  • DOI: https://doi.org/10.1007/BF02106984

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