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New characterizations of real hypersurfaces with isometric Reeb flow in the complex quadric

Volume 164 / 2021

Zejun Hu, Jiabin Yin Colloquium Mathematicum 164 (2021), 211-219 MSC: Primary 53C24, 53C40; Secondary 53C42, 53C55. DOI: 10.4064/cm8075-12-2019 Published online: 4 September 2020


We prove an integral inequality for compact orientable real hypersurfaces of the complex quadric $Q^n\ (n\ge 3)$ in terms of their shape operator $S$ and Reeb vector field $\xi $. As direct consequences, we obtain new characterizations for real hypersurfaces of $Q^n$ with isometric Reeb flow. Such hypersurfaces have been classified by J. Berndt and Y. J. Suh [Int. J. Math. 24 (2013), art. 1350050, 18 pp.].


  • Zejun HuSchool of Mathematics and Statistics
    Zhengzhou University
    Zhengzhou 450001
    People’s Republic of China
  • Jiabin YinSchool of Mathematical Sciences
    Xiamen University
    Xiamen 361005
    People’s Republic of China

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