Abstract
In this work, generalized weakly [Formula: see text]-symmetric space-times [Formula: see text] are investigated, where [Formula: see text] is any symmetric [Formula: see text] tensor. It is proved that, in a nontrivial [Formula: see text] space-time, the tensor [Formula: see text] has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time [Formula: see text] to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric [Formula: see text] tensor to be Einstein or perfect fluid space-times are provided.
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