The authors consider Ricci solitons on \((\kappa, \mu)\)-almost cosymplectic manifolds and address questions about their existence. They consider results by X. Chen [Bull. Belg. Math. Soc. Simon Stevin, 25, 305–319 (2018; Zbl 1395.53085)], who initially argued that Ricci solitons do not exist on almost cosymplectic \((\kappa, \mu)\)-manifolds, but later, in [“Ricci solitons in almost \(f\)-cosymplectic manifolds”, Preprint, arXiv:1801.04398v2], claimed nonexistence only for a specific range of \(\kappa\) and \(\mu\).
In the current paper the authors provide an example of a Ricci soliton on an almost cosymplectic \((\kappa, \mu)\) within the specified range of Chen’s second paper. Chen argued that Ricci solitons did not exist on \((\kappa, \mu)\)-manifolds with \(\kappa < 0\) and \(-\frac{1}{2} < \mu < 0\) and \(\mu = 0\). The authors here prove the existence of an expanding Ricci soliton on a \((\kappa, \mu)\)-almost cosymplectic manifold with \(\kappa < 0\).
The authors also identify and correct other errors in Chen’s second paper. In addition, they consider existence problems of particular potential vector fields on \((\kappa, \mu)\)-almost cosymplectic manifolds that admit Ricci solitons.