On a Property of Quasi-Kähler Manifolds

We prove that if a quasi-Kähler manifold satisfies the $\eta$-quasi-umbilic quasi-Sasakian hypersurface axiom, then it is a Kähler manifold. We also prove that the quasi-Sasakian structure on an $\eta$-quasi-umbilical hypersurface in a quasi-Kähler manifold is either cosymplectic or homothetic to the Sasakian structure.