Some Characterization Results on Generalized Weakly Symmetric Kenmotsu Manifolds

‎In this paper‎, ‎we prove that every non-Einstein generalized weakly symmetric Kenmotsu manifold is generalized pseudo symmetric by showing that $A_i=‎ -‎2\eta$ and $B_i = D_i =‎ -‎\eta$ (when $i=1‎, ‎2$)‎. ‎Then‎‎‎, ‎we give a necessary condition for Kenmotsu manifolds to be generalized weakly symmetric‎. ‎We also demonstrate that weakly Ricci-symmetric Kenmotsu manifolds are Einstein‎. ‎Thereafter‎‎‎, ‎we illustrate that for every generalized weakly Ricci-symmetric Kenmotsu manifold with non-constant scalar curvature which satisfies $X(r)‎ +‎2 (r‎ + ‎n(n-1))\eta(X) = 0$‎, ‎the associated $1$-forms satisfy $A_1=\frac{A_2}{(n-1)} =‎ -‎2\eta$ and ${B_1}={D_1} =\frac{B_2}{(n-1)} =\frac{D_2}{(n-1)} =‎- ‎\eta$‎. ‎Finally, ‎we ‎give ‎an ‎example ‎which ‎verifies ‎our ‎results obtained in previous ‎sections.‎