Closed Conformal Vector Fields in Gradient Einstein Solitons

We investigate gradient Einstein solitons admitting closed conformal vector fields. Under constant scalar curvature, we establish rigidity results showing that complete solitons with non-parallel closed conformal vector fields are isometric to Euclidean space. In the non-compact case, we prove that solitons with homothetic closed conformal vector fields are locally conformally flat in dimension four and possess a harmonic Weyl tensor in higher dimensions. Furthermore, we obtain a classification result, showing that such solitons admit a warped product structure with a one-dimensional base and space form fibers.