Ricci-Bourguignon Soliton on Quasi-Para Sasakian Manifolds
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Abstract
In the present article, we investigate Ricci–Bourguignon solitons on three-dimensional quasi-para-Sasakian manifolds equipped with a pseudo-Riemannian metric. We derive explicit conditions on the Ricci tensor under the assumption that the soliton potential vector field is affine conformal. It is shown that, in this setting, the Ricci tensor becomes a conformal quadratic Killing tensor. Furthermore, we prove that if the potential vector field is affine conformal, then it coincides with a Jacobi vector field along the geodesics generated by the Reeb vector field, and the Reeb vector field itself is geodesic. Finally, we establish that when the soliton vector field is conformal and the scalar curvature is harmonic, the manifold is Einstein and locally isometric to the three-dimensional hyperbolic space. These results highlight strong geometric rigidity phenomena for Ricci–Bourguignon solitons on quasi- para-Sasakian manifolds.
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