The Z-Tensor on Almost Co-Kählerian Manifolds Admitting Riemann Soliton Structure

A Riemann soliton (RS) is a natural generalization of a Ricci soliton structure on pseudo-Riemannian manifolds. This work aims at investigating almost co-Kählerian manifolds (ACKM) 2n+1 whose metrics are Riemann solitons utilizing the properties of the Z-tensor. For instance, the consequences of recurrency of the Z-tensor on almost co-Kählerian manifolds admitting a Riemann soliton structure are investigated. Finally, an appropriate example establishes the reality of an RS over three dimensions (ACKM) 2n+1.