Geometrical Consequences of Conformal Symmetries in Gradient Schouten Solitons

This study explores the conformal geometry of gradient Schouten solitons characterized by constant scalar curvature, which represents a notable extension of the Einstein equation. We prove that a closed gradient Schouten soliton equipped with a non-trivial closed conformal vector is isometric to the round sphere. In the sequel, we prove that a non-compact gradient Schouten solitons admitting a non-trivial gradient conformal vector field are isometric to a Euclidean space or a warped product I×ξMm−1 of an interval I and an Einstein manifold Mm−1 provided that scalar curvature of Mm−1 is constant. Moreover, the same results are proved when the soliton vector field of the gradient Schouten soliton is divergence-free.