On a Property of Quasi-Kähler Manifolds

We prove that if a quasi-Kähler manifold satisfies the \(\eta\) -quasi-umbilical quasi-Sasakian hypersurfaces 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 a Sasakian structure.