Communications of the
Korean Mathematical Society CKMS

The purpose of this note is to introduce a type of Riemannian manifold called an almost quasi Ricci symmetric manifold and investigate the several properties of such a manifold on which some geometric conditions are imposed. And the existence of such a manifold is ensured by a proper example.

Keywords: Almost quasi Ricci symmetric manifolds, Einstein, Ricci-flat, quasi Ricci symmetric manifold, conformally flat, quasi-Einstein, a space of quasi-constant curvature, torse-forming vector field, product manifold, cyclic Ricci tensor, Codazzi type

MSC numbers: Primary 53A55, 53B20