Cyclic semiparallel Ricci tensor for harmonic curvature in the complex quadric

Abstract

AbstractWe introduce the notion of harmonic curvature for real hypersurfaces in the complex quadric . First, we prove that the unit normal vector field N on real hypersurfaces in with harmonic curvature is singular, that is, ‐principal or ‐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 .