Year: 2024
Type: article
Abstract: : Let $M$ be a Fano compactification of a semisimple complex Lie group $G$ and $\omega_0$ a $K\times K$-invariant metric in $2\pi c_1(M)$, where $K$ is a maximal compact subgroup of $G$. Then we prove that the solution of K\"ahler-Ricci flow with $\omega_0$ as an initial metric on $M$, is of type II, if $M$ admits no K\"ahler-Einstein metrics. As an application, we found two Fano compactifications of $\mathrm{SO}_4(\mathbb{C})$ and one Fano compactification of $\mathrm{Sp}_4(\mathbb{C})$, on which the K\"ahler-Ricci flow will develop singularities of type II. To the authors' knowledge, these are the first examples of Ricci flow with singularities of type II on Fano manifolds in the literature.
Source: American Journal of Mathematics
Authors: Yan Li, Gang Tian, Xiaohua Zhu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1376109390, G2864987927, G3446960876
OpenAlex ID: W4404597168