  The present paper deals with the proper existence of a generalized class of
recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have
established the proper existence of various generalized notions of recurrent
manifolds. For this purpose we have presented a metric and computed its
curvature properties and finally we have obtained the existence of a new class
of semi-Riemannian manifolds which are non-recurrent but hyper-generalized
recurrent, Ricci recurrent, conharmonically recurrent, manifold of recurrent
curvature 2-forms and semisymmetric; not weakly symmetric but weakly Ricci
symmetric, conformally weakly symmetric and conharmonically weakly symmetric;
non-Einstein but Ricci simple; do not satisfy $P\cdot P =0$ but fulfills the
condition $P \cdot P = -\frac{1}{3}Q(S, P)$, $P$ being the projective curvature
tensor.

Differential Geometry