Real hypersurfaces in the complex quadric with commuting Ricci tensor

Abstract

We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric $Q^m=S{O}_{m+2}/S{O}_{m}S{O}_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\mathfrak{A}$-principal or $\mathfrak{A}$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^m=S{O}_{m+2}/S{O}_{m}S{O}_2$ with commuting Ricci tensor.

References in corpus (1)

• Totally geodesic submanifolds of the complex quadric

Cited by in corpus (1)

• Real hypersurfaces of complex quadric in terms of star-Ricci tensor