论文标题
RICCI流动溶液与Taub-nut的收敛性
Convergence of Ricci flow solutions to Taub-NUT
论文作者
论文摘要
我们研究以SU（2）的cohomosity-1 Metric-1 $ g_ {0} $从$ \ mathbb {r}^{4} $带有单调翘曲系数，其对任何Hypersphere的限制是Berger Metric的限制。如果$ g_ {0} $具有HOPF纤维，曲率由轨道的大小控制，并且比HopF纤维正交的抛物面比抛物面更快，则流向taub-nut $ g _ {\ mathsf {\ mathsf {tnut}} $ in Infinite in Indite in Indite in Infinite in Indite in Indite in Indite in Indite in Indite in Indite in Indite in Indite in Indite。当$ g_ {0} $渐近平坦时，我们还对长期行为进行了分类。为了识别无限时间的奇异模型，我们获得了$ g _ {\ mathsf {tnut}} $的唯一性结果。
We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric $g_{0}$ on $\mathbb{R}^{4}$ with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If $g_{0}$ has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric $g_{\mathsf{TNUT}}$ in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when $g_{0}$ is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for $g_{\mathsf{TNUT}}$.
