Abstract

In this paper we define and study a new kind of quasi-constant curvature called generalized super-quasi-constant curvature. The existence of a generalized super quasi-constant curvature has also been verified by an example. We prove that a super quasi-umbilical hypersurface of a constant curvature manifold is a generalized super quasiconstant curvature manifold. Furthermore, it is proved that manifold of generalized super quasi-constant curvature is a super quasi-Einstein manifold. We have also introduced a sufficient condition to be a Super quasi-Einstein manifold. Lastly, we construct an example super quasi-Einstein manifold in general form.