AI 中文总结
该研究针对闭定向负曲率黎曼流形的定向标架流，在不同维数下改进了挤压条件，证明了对应维数下标架流的遍历性，解决了Brin的四分之一挤压猜想并拓展了例外维数的结果。
AI 中文摘要
设$(M^n,g)$为闭定向负曲率黎曼流形，已知此类流形的定向标架流对所有奇数维$n\neq7$均遍历。我们证明：当$n=4$及$n\not\neq134$且$n\not\neq2\bmod4$时，严格1/4挤压蕴含定向标架流的遍历性；当$n\not\neq0\bmod4$且$n\not\neq12$时，5/13挤压蕴含遍历性；在例外维数7、8、134时，分别在严格0.4661…、0.5358…、2/5挤压下证明遍历性，这些结果大幅改进了Cekić–Lefeuvre–Moroianu–Semmelmann得到的对应界。
英文摘要
Let $(M^n,g)$ denote a closed oriented negatively curved Riemannian manifold. For such manifolds, the oriented frame flow is known to be ergodic for all odd dimensions $n\neq7$. We prove Brin's quarter-pinching conjecture when $n=4$, and when $n\equiv2\pmod4$ with $n\neq134$: strict $1/4$-pinching implies ergodicity of the oriented frame flow. We also prove that if $n\equiv0\pmod4$ and $n\geq12$, then $5/13$-pinching implies ergodicity. In the exceptional dimensions $7$, $8$, and $134$, we prove ergodicity under strict $0.4661...$-, $0.5358...$-, and $2/5$-pinching, respectively. These results substantially improve the corresponding bounds obtained by Cekić--Lefeuvre--Moroianu--Semmelmann.
Comments46 pages
