Real Hypersurfaces in the Complex Quadric with Reeb Parallel Ricci Tensor

Abstract

First we introduce the notion of commuting and parallel Ricci tensor for real hypersurfaces in the complex quadric $$Q^m = SO_{m+2}/SO_2SO_m$$. Then, according to the $$\mathfrak {A}$$-principal or the $$\mathfrak {A}$$-isotropic unit normal vector field N, respectively, we give a classification of real hypersurfaces in $$Q^m = SO_{m+2}/SO_2SO_m$$ with Reeb parallel Ricci tensor.