3-Dimensional real hypersurfaces with transversal $\eta$-Killing Ricci tensor field of a complex space form

Abstract

We classify real hypersurfaces of a non-flat complex space form of complex dimension 2 satisfying the condition that the Ricci tensor S is the transversal Killing tensor field on the direction of the structure vector field $\xi$ and $S\xi = \beta\xi$ where $\beta$ is a function.