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

Abstract

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 ‐tensor. For instance, the consequences of recurrency of the ‐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.