Nonnegatively and Positively Curved Invariant Metrics on Circle Bundles
نویسندگان
چکیده
We derive and study necessary and sufficient conditions for an S-bundle to admit an invariant metric of positive or nonnegative sectional curvature. In case the total space has an invariant metric of nonnegative curvature and the base space is odd dimensional, we prove that the total space contains a flat totally geodesic immersed cylinder. We provide several examples, including a connection metric of nonnegative curvature on the trivial bundle S×S that is not a product metric.
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