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- W4288043515 abstract "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 $pi: mathrm{SO}(3), mathrm{S}^3 hookrightarrow cal P rightarrow B$ 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." @default.
- W4288043515 created "2022-07-27" @default.
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- W4288043515 date "2022-07-21" @default.
- W4288043515 modified "2023-10-18" @default.
- W4288043515 title "The Petersen--Wilhelm conjecture on principal bundles" @default.
- W4288043515 doi "https://doi.org/10.48550/arxiv.2207.10749" @default.
- W4288043515 hasPublicationYear "2022" @default.
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