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

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