Cyclic semiparallel Ricci tensor for harmonic curvature in the complex quadric

초록

We introduce the notion of harmonic curvature for real hypersurfaces in the complex quadric Q(m) = SOm+2/SOmSO2. First, we prove that the unit normal vector field N on real hypersurfaces in Q(m) with harmonic curvature is singular, that is, 21-principal or 21-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 Q(m) = SOm+2/SOmSO2.

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