AI 中文总结
该研究关联李群左不变广义度量的广义里奇曲率与度量李代数的里奇曲率，证明相关流的子收敛性，建立标准 Bismut 平坦度量的动力学稳定性并构造非标准不稳定例子。
AI 中文摘要
我们将李群上左不变广义度量的广义里奇曲率与特定度量李代数的里奇曲率关联起来。作为应用，我们证明了在具有半正定基灵型的单连通李群上，重标度广义里奇流子收敛到膨胀广义里奇孤子。在相同假设下，还证明了 pluriclosed 流子收敛到膨胀 pluriclosed 孤子。我们进一步证明，左不变 Bismut-Ricci 平坦度量是幺模李群上广义标量曲率泛函的临界点。鉴于此，我们在紧单连通半单李群上建立了所谓标准双不变、Bismut 平坦度量的广义里奇流的动力学稳定性，并构造了非标准的动力学不稳定 Bismut 平坦度量的例子。
英文摘要
We relate the generalized Ricci curvature of left-invariant generalized metrics on a Lie group with the Ricci curvature of certain metric Lie algebras. As an application, we prove subconvergence of rescaled generalized Ricci flows to expanding generalized Ricci solitons on simply connected Lie groups with positive semi-definite Killing form. Under the same hypotheses, subconvergence of pluriclosed flows to expanding pluriclosed solitons is also shown. We further prove that left-invariant Bismut-Ricci flat metrics arise as critical points for the generalized scalar curvature functional on unimodular Lie groups. In view of this, we establish dynamical stability for the generalized Ricci flow of so-called standard bi-invariant, Bismut-flat metrics on compact, simply connected, semisimple Lie groups and construct examples of dynamically unstable Bismut-flat metrics which are non-standard.
Comments36 pages, comments welcome!
