Gradient pseudo‐Ricci solitons of real hypersurfaces.

Let M be a real hypersurface of a complex space form Mn(c)$M^n(c)$, c≠0$c\ne 0$. Suppose that the structure vector field ξ of M is an eigen vector field of the Ricci tensor S, Sξ=βξ$S\xi =\beta \xi$, β being a function. We study on M, a gradient pseudo‐Ricci soliton (M,g,f,λ,μ$M,g,f,\lambda ,\mu$) that is an extended concept of gradient Ricci soliton, closely related to pseudo‐Einstein real hypersurfaces. When n≥3$n\ge 3$, we show that M is a Hopf hypersurface. [ABSTRACT FROM AUTHOR]