论文标题
彼得森 - 威廉·猜想的主要捆绑包
The Petersen--Wilhelm conjecture on principal bundles
论文作者
论文摘要
本文研究了$ \ mathrm {s}^3，\ mathrm {so}（3）$ principal捆绑包的cheeger变形，以获取正面曲率累积指标的条件。我们尤其得出结论，彼得森（Petersen）的更强大版本 - 对主要捆绑包的Wilhelm纤维维度猜想。我们证明了任何$π：\ mathrm {so}（3），\ mathrm {s}^3 \ hookrightarrow \ cal p \ cal p \ rightarrow b $ thim bugry bum principal bunconal buncally bunctal thiked Curved base基地承认，如果，则仅当肥皂水尤其是$ \ dim b beg beg beg be b $ \ geq 4 $。该证明将``良好的三重''概念结合在一起，原因是Munteanu和Tapp \ cite {tappMunteAnu2}，以及chaves-derdzisnki-rigas类型的条件与非负曲率。此外，对其他类别的淹没验证了猜想。
This paper studies Cheeger deformations on $\mathrm{S}^3, \mathrm{SO}(3)$ principal bundles to obtain conditions for positive sectional curvature submersion metrics. We conclude, in particular, a stronger version of the Petersen--Wilhelm fiber dimension conjecture to the class of principal bundles. We prove any $π: \mathrm{SO}(3), \mathrm{S}^3 \hookrightarrow \cal P \rightarrow B$ principal bundle over a positively curved base admits a metric of positive sectional curvature if, and only if, the submersion is fat, in particular, $\dim B \geq 4$. The proof combines the concept of ``good triples'' due to Munteanu and Tapp \cite{tappmunteanu2}, with a Chaves--Derdzisnki--Rigas type condition to nonnegative curvature. Additionally, the conjecture is verified for other classes of submersions.
