论文标题
在Oeljeklaus-Toma歧管上的多裂流上
On the pluriclosed flow on Oeljeklaus-Toma manifolds
论文作者
论文摘要
我们研究了Oeljeklaus-toma歧管上的多裂流。我们在oeljeklaus-toma歧管上参数左右多数指标，并将其分类为将多个流动流的代数孤子升至通用覆盖物上的代数孤子。我们进一步表明，从剩余的多元型公制开始的多腔流具有长期解决方案$ω_t$，曾经在Gromov-Hausdorff Sense中标准化了折叠成圆环。此外，$ \ tfrac {1} {1+t}ω_t$的提升到cheeger-gromov中的普遍覆盖物中的普遍覆盖率收敛于$（\ m athbb h^r \ times \ times \ mathbb c^s，\ tilde}索利顿。
We investigate the pluriclosed flow on Oeljeklaus-Toma manifolds. We parametrize left-invariant pluriclosed metrics on Oeljeklaus-Toma manifolds and we classify the ones which lift to an algebraic soliton of the pluriclosed flow on the universal covering. We further show that the pluriclosed flow starting from a left-invariant pluriclosed metric has a long-time solution $ω_t$ which once normalized collapses to a torus in the Gromov-Hausdorff sense. Moreover the lift of $\tfrac{1}{1+t}ω_t$ to the universal covering of the manifold converges in the Cheeger-Gromov sense to $(\mathbb H^r\times\mathbb C^s, \tildeω_{\infty})$ where $\tildeω_{\infty}$ is an algebraic soliton.
