On pseudo-Einstein ruled real hypersurfaces in complex space forms

Abstract

In this paper we define the new notion of pseudo-Einstein ruled real hypersurfaces, which are foliated by the leaves of pseudo-Einstein complex hypersurfaces in complex space forms $M_{n}(c), c ≠ 0$. Also we want to give a new characterization of this kind of Pseudo-Einstein ruled real hypersurfaces in terms of the Ricci tensor and the certain integrability condition defined on the orthogonal distribution $T_{0}$ in $M_{n}(c)$.