In this paper, we have researched the necessary and sufficient conditions for a manifold to be weakly symmetric and weakly Ricci–symmetric and examined the conditions over 1–forms involved in the definitions of weakly symmetric and weakly Ricci–symmetric conditions. We have evaluated some certain results of situations in which a weakly symmetric manifold is with parallel or cyclic Ricci tensor. Finally, an example is used to demonstrate that the method presented in this paper is effective.
Key words: manifold, Weakly Symmetric, Weakly Ricci Symmetric.
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