Ricci tensor of Hopf hypersurfaces in a complex space form

Abstract

We classify Hopf hypersurfaces in a non-flat complex space form whose Ricci tensor S satisfies g((∇ X S)X, ξ) = 0 for any vector field X tangent to ξ, where ξ is the structure vector field. We also classify real hypersurfaces with transversal Killing Ricci tensor satisfying Sξ = βξ for some function β.