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.

中文翻译：

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关于弱循环广义Z对称流形

在本文中，我们定义了（0,2）型对称张量Z并将其称为广义Z张量。我们研究了弱循环广义Z对称流形，并证明它是广义拟爱因斯坦流形。我们获得了1形式和的消失的条件。我们进一步发现条件是Ricci半对称流形。最后，证明了在这种流形中半对称和Weyl半对称是等效的。