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

Rongsheng Ma and Donghe Pei ()
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Rongsheng Ma: School of Science, Yanshan University, Qinhuangdao 066004, China
Donghe Pei: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Mathematics, 2022, vol. 11, issue 1, 1-14

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.

Keywords: Reeb-flow-invariant ?-Ricci operator; Reeb-parallel ?-Ricci operator; semi-symmetric ?-Ricci tensor; singular-unit normal vector field (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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