On Non‐Compact Extended Bach Solitons

ABSTRACT We study the characterization of non‐compact solitons of the extended Bach flow, known as an extended Bach soliton. We prove that a weakly conformally flat extended Bach soliton with harmonic Weyl tensor is Bach‐flat and the potential vector field is conformal. In the case of an extended gradient Bach soliton, we impose certain regularity conditions on the potential function, Ricci curvature constraints on , and assume that the Weyl tensor is harmonic, to deduce that is trivial and Bach‐flat.