Sphere Bundles with 1/4-pinched Fiberwise Metrics
نویسنده
چکیده
We prove that all smooth sphere bundles that admit fiberwise 1/4-pinched metrics are induced bundles of vector bundles, so their structure groups reduce from DIFF(Sn) to O(n + 1). This result implies the existence of many smooth Sn-bundles over Sk that do not support strictly 1/4-pinched positively curved Riemannian metrics on their fibers.
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