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The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric

Author

Listed:
  • Rongsheng Ma

    (School of Science, Yanshan University, Qinhuangdao 066004, China)

  • Donghe Pei

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

Abstract

We study the ∗-Ricci operator on Hopf real hypersurfaces in the complex quadric. We prove that for Hopf real hypersurfaces in the complex quadric, the ∗-Ricci tensor is symmetric if and only if the unit normal vector field is singular. In the following, we obtain that if the ∗-Ricci tensor of Hopf real hypersurfaces in the complex quadric is symmetric, then the ∗-Ricci operator is both Reeb-flow-invariant and Reeb-parallel. As the correspondence to the semi-symmetric Ricci tensor, we give a classification of real hypersurfaces in the complex quadric with the semi-symmetric ∗-Ricci tensor.

Suggested Citation

  • Rongsheng Ma & Donghe Pei, 2022. "The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:90-:d:1015096
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    References listed on IDEAS

    as
    1. Rongsheng Ma & Donghe Pei, 2019. "Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-7, December.
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