(\eta-\)Ricci solitons on contact pseudo-metric manifolds

In this paper, we prove that a Sasakian pseudo-metric manifold which admits an \(\eta-\)Ricci soliton is an \(\eta-\)Einstein manifold, and if the potential vector field of the \(\eta-\)Ricci soliton is not a Killing vector field then the manifold is \(\mathcal{D}-\)homothetically fixed, and the vector field leaves the structure tensor field invariant. Next, we prove that a \(K-\)contact pseudo-metric manifold with a gradient \(\eta-\)Ricci soliton metric is \(\eta-\)Einstein. Moreover, we study contact pseudo-metric manifolds admitting an \(\eta-\)Ricci soliton with a potential vector field point-wise colinear with the Reeb vector field. Finally, we study gradient \(\eta-\)Ricci solitons on \((\kappa, \mu)\)-contact pseudo-metric manifolds.