Generalized Weakly Symmetric Sasakian Manifolds

In this parer, we give a necessary condition for sasakian manifolds to be generalized weakly symmetric. we prove the odddimensional spheres are the only generalized weakly symmetric sasakian manifolds. then, we show that generalized weakly ricci-symmetric sasakian manifolds are einstein. thereafter, we define the sense of weakly parallel riemannian submanifolds and show that every weakly parallel invariant submanifold of a sasakian manifold is totally geodesic. finally, we provide some examples which verify our main results.