关于 Kähler 流形上酉标架流的遍历性
On the ergodicity of unitary frame flows on Kähler manifolds
AI总结：
本文研究了负曲率闭Kähler流形上的酉标架流，证明了在复维数 $m\geq6$ 为偶数且 $m\neq28$ 时，若流形具有特定的负夹挤全纯截面曲率，则该流遍历且混合，将Brin-Gromov的奇维结论推广至偶维。
摘要：
设 $(M,g,J)$ 为具有负截面曲率且复维数 $m := \dim_{\mathbb{C}} M \geq 2$ 的闭 Kähler 流形。本文研究了酉标架流，即标架流限制在酉标架的主 $\mathrm{U}(m)$-丛 $F_{\mathbb{C}}M$ 上。我们证明，若 $m \geq 6$ 为偶数且 $m \neq 28$，则存在 $λ(m) \in (0, 1)$，使得当 $(M, g, J)$ 具有负的 $λ(m)$-夹挤全纯截面曲率时，酉标架流是遍历且混合的。常数 $λ(m)$ 满足 $λ(6) = 0.9330...$，$\lim_{m \to +\infty} λ(m) = \tfrac{11}{12} = 0.9166...$，且 $m \mapsto λ(m)$ 递减。此结果将 Brin-Gromov 关于奇复维数负曲率紧 Kähler 流形酉标架流遍历性的结论推广至偶维情形。
英文摘要：
Let $(M,g,J)$ be a closed Kähler manifold with negative sectional curvature and complex dimension $m := \dim_{\mathbb{C}} M \geq 2$. In this article, we study the unitary frame flow, that is, the restriction of the frame flow to the principal $\mathrm{U}(m)$-bundle $F_{\mathbb{C}}M$ of unitary frames. We show that if $m \geq 6$ is even, and $m \neq 28$, there exists $λ(m) \in (0, 1)$ such that if $(M, g, J)$ has negative $λ(m)$-pinched holomorphic sectional curvature, then the unitary frame flow is ergodic and mixing. The constants $λ(m)$ satisfy $λ(6) = 0.9330...$, $\lim_{m \to +\infty} λ(m) = \tfrac{11}{12} = 0.9166...$, and $m \mapsto λ(m)$ is decreasing. This extends to the even-dimensional case the results of Brin-Gromov who proved ergodicity of the unitary frame flow on negatively-curved compact Kähler manifolds of odd complex dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
