Some special Z-symmetric manifolds with applications to space-times and Ricci solitons

Abstract

This work aims to investigate various properties of some special Z-symmetric manifolds and their applications on space-times. Having an important place of the study, classifications of second-order symmetric tensor fields on space-times and holonomy theory are considered. Z-symmetric manifolds in the holonomy structure are investigated and some results are obtained. Various special vector fields are examined on Z-recurrent and weakly Z-symmetric manifolds and some relations associated with the eigenvector structure of the Z-tensor are found. In addition, several examples related to the outcomes of the study are given. Finally, some links between the Z-tensor and Ricci solitons on space-times are determined.