η-Ricci-Bourguignon solitons on K-paracontact and paracontact metric (κ≠−1, µ)-manifolds

Abstract

In this study, we focus on $\left( 2n+1\right) $-dimensional $K$-paracontact manifolds admitting $\eta $-Ricci-Bourguignon solitons and gradient $\eta $%-Ricci-Bourguignon solitons. We then completely present the classification of a $\left( 2n+1\right) $-dimensional paracontact metric $\left( \kappa \neq -1\text{, }\mu \right) $-manifold that admits a gradient $\eta $%-Ricci-Bourguignon soliton. Finally, we construct examples that provide our results.