论文标题
缩小梯度kähler-icci孤子的独特性
Uniqueness of shrinking gradient Kähler-Ricci solitons on non-compact toric manifolds
论文作者
论文摘要
我们表明，为了生物形态，最多有一个完整的$ t^n $ invariant缩小梯度Kähler-ricci soliton在非紧凑型曲折歧管上$ m $。如果RICCI曲率受到界限，并且如果soliton vector字段位于$ t^n $的lie algebra $ \ mathfrak {t} $中，我们还可以建立唯一性而不假设$ t^n $ invariance。作为一个应用程序，我们表明，在等轴测过程中，独特的完整缩小梯度Kähler-ricci soliton在$ \ mathbb {cp}^{1} \ times \ times \ mathbb {cp {cp {cp}^{cp} \ mathbb {c} $上是与fubini-Study study intric oon $ \ nath $ \ mathb} cp} cp} cp} {cp} {cp} {cp^$ $ \ mathbb {c} $上的Euclidean Metric。
We show that, up to biholomorphism, there is at most one complete $T^n$-invariant shrinking gradient Kähler-Ricci soliton on a non-compact toric manifold $M$. We also establish uniqueness without assuming $T^n$-invariance if the Ricci curvature is bounded and if the soliton vector field lies in the Lie algebra $\mathfrak{t}$ of $T^n$. As an application, we show that, up to isometry, the unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on $\mathbb{CP}^{1} \times \mathbb{C}$ is the standard product metric associated to the Fubini-Study metric on $\mathbb{CP}^{1}$ and the Euclidean metric on $\mathbb{C}$.
