Generalized Killing Ricci tensor for real hypersurfaces in the complex quadric

Abstract

First we introduce a new notion of generalized Killing Ricci tensor which is equivalent to the notion of cyclic parallel Ricci tensor for real hypersurfaces in the complex quadric 𝑄 𝑚 = 𝑆𝑂 𝑚+2 ∕𝑆𝑂 𝑚 𝑆𝑂 2 . Next, in terms of 𝔄-principal or 𝔄-isotropic unit normal vector fields we give a complete classification of real hypersurfaces in 𝑄 𝑚 = 𝑆𝑂 𝑚+2 ∕𝑆𝑂 𝑚 𝑆𝑂 2 with cyclic parallel Ricci tensor.