Real Hypersurfaces in the Complex Hyperbolic Quadric with Parallel Ricci Tensor

Abstract

We introduce the notion of parallel Ricci tensor for real hypersurfaces in the complex hyperbolic quadric $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$ . According to the $$\mathfrak {A}$$ -principal or the $$\mathfrak {A}$$ -isotropic unit normal vector field N, we give a complete classification of real hypersurfaces in $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$ with Ricci parallelism.