On mixed super quasi-Einstein manifolds

Abstract

In this paper, mixed super quasi-Einstein manifolds (MS(QE)n) have been defined. The existence theorem and an example have been provided and the relations between the associated scalars have been established. As well, manifolds of mixed super quasi-constant curvature are defined, and it is shown that quasi conformally flat, conformally flat, conharmonically flat and projectively flat MS(QEn) are manifolds of mixed super quasi-constant curvature. Further, super quasi-umbilical hypersurfaces of Riemannian manifolds have been defined and it is proved that a super quasi-umbilical hypersurface of a Euclidean space is MS(QE)n. M.S.C. 2000: 53C25.