Uniqueness of shrinking gradient Kähler–Ricci solitons on non?compact toric manifolds

We show that, up to biholomorphism, there is at most one complete T n $T^n$ -invariant shrinking gradient Kähler–Ricci soliton on a non-compact toric manifold M. also establish uniqueness without assuming -invariance if the Ricci curvature bounded and vector field lies in Lie algebra t $\mathfrak {t}$ of . As an application, we isometry, unique with scalar C P 1 × $\mathbb {C}\mathbb {P}^{1} \times \mathbb {C}$ standard product metric associated Fubini–Study {P}^{1}$ Euclidean