Cyclic semiparallel Ricci tensor for harmonic curvature in the complex quadric

Young Jin Suh

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3630-3651

Abstract: We introduce the notion of harmonic curvature for real hypersurfaces in the complex quadric Qm=SOm+2/SOmSO2$Q^m = SO_{m+2}/SO_mSO_2$. First, we prove that the unit normal vector field N on real hypersurfaces in Qm$Q^m$ with harmonic curvature is singular, that is, A$\mathfrak {A}$‐principal or A$\mathfrak {A}$‐isotropic. Next by using a new notion of cyclic semiparallel Ricci tensor, we give a new result on real hypersurfaces with harmonic curvature and constant mean curvature in Qm=SOm+2/SOmSO2$Q^m = SO_{m+2}/SO_mSO_2$.

Date: 2023
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https://doi.org/10.1002/mana.202100551

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