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A rigidity theorem for centroaffine Chebyshev hyperovaloids

Volume 157 / 2019

Xiuxiu Cheng, Zejun Hu, Zeke Yao Colloquium Mathematicum 157 (2019), 133-141 MSC: Primary 53A15; Secondary 53C24, 53C42. DOI: 10.4064/cm7382-6-2018 Published online: 15 March 2019

Abstract

In this note, we investigate centroaffine hyperovaloids. We first establish an integral formula under the additional Chebyshev condition. Then, combining the integral formula with our recent classification of locally strongly convex centroaffine hypersurfaces with parallel traceless difference tensor [J. Geom. Anal. 28 (2018), 643–655], we obtain a rigidity theorem which shows that if a centroaffine Chebyshev hyperovaloid has nonnegative centroaffine sectional curvatures then it must be an ellipsoid.

Authors

  • Xiuxiu ChengSchool of Mathematics and Statistics
    Zhengzhou University
    Zhengzhou 450001, People’s Republic of China
    e-mail
  • Zejun HuSchool of Mathematics and Statistics
    Zhengzhou University
    Zhengzhou 450001, People’s Republic of China
    e-mail
  • Zeke YaoSchool of Mathematics and Statistics
    Zhengzhou University
    Zhengzhou 450001, People’s Republic of China
    e-mail

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