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

2020/10/01 by Cifarelli, Charles · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2010.00166

Abstract

We show that, up to biholomorphism, there is at most one complete Tⁿ-invariant shrinking gradient Kähler-Ricci soliton on a non-compact toric manifold M. We also establish uniqueness without assuming Tⁿ-invariance if the Ricci curvature is bounded and if the soliton vector field lies in the Lie algebra \mathfrakt of Tⁿ. As an application, we show that, up to isometry, the unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on \mathbbCP¹ × ℂ is the standard product metric associated to the Fubini-Study metric on \mathbbCP¹ and the Euclidean metric on ℂ.

Cited by

• Toric geometry of generalized Kähler-Ricci solitons

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