Gradient pseudo-Ricci solitons of real hypersurfaces

Abstract

Let $M$ be a real hypersurface of a complex space form $M^n(c)$, $c\ne 0$. Suppose that the structure vector field $\xi$ of $M$ is an eigen vector field of the Ricci tensor $S$, $S\xi =\beta \xi$, $\beta$ being a function. We study on $M$, a gradient pseudo-Ricci soliton as an extended concept of Ricci soliton, closely related to pseudo-Einstein real hypersurfaces. We show that a $3$-dimensional ruled real hypersurface of $M^2(c),c<0$ admits a non-trivial gradient pseudo-Ricci soliton.

References in corpus (1)

• Hopf Hypersurfaces of Small Hopf Principal Curvature in CH^2