Abstract
In this paper, we define a (0,2)-type symmetric tensor Z and called it a generalized Z tensor. We study weakly cyclic generalized Z-symmetric manifold and prove that it is a generalized quasi-Einstein manifold. We have obtained a condition for vanishing of sum of 1-forms. We further find a condition to be a Ricci semisymmetric manifold. Finally, it is shown that the semisymmetry and Weyl semisymmetry are equivalent in such a manifold.
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