A classification of cyclic Ricci semi-symmetric hypersurfaces in the complex hyperbolic quadric

Abstract

In this paper, the notion of cyclic Ricci semi-symmetric real hypersurfaces in the complex hyperbolic quadric ${Q^m}^*={SO^0_{2,m}/SO_2 SO_m}$ is introduced. Under the assumption of singular normal vector field $N$, we have two cases, that is, normal vector field $N$ is either $\mathfrak A$-principal or $\mathfrak A$-isotropic. Even though, in the case of $\mathfrak A$-principal, we proved that there does not exist a real hypersurface in the complex hyperbolic quadric ${Q^m}^*={SO^0_{2,m}/SO_2 SO_m}$ satisfying the cyclic Ricci semi-symmetric. But on the other case, we proved
existence of real hypersurfaces with the same condition.