Mabuchi Kähler solitons versus extremal Kähler metrics and beyond

Abstract Using the Yau–Tian–Donaldson type correspondence for ‐solitons established by Han–Li, we show that a smooth complex ‐dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than . Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal Kähler metrics on Fano manifolds. An extension of this correspondence to ‐solitons is also obtained.