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MiS Preprint

Nonnegatively and Positively Curved Invariant Metrics on Circle Bundles

Krishnan Shankar, Kristopher Tapp and Wilderich Tuschmann


We derive and study necessary and sufficient conditions for an $S^1$ bundle to admit an invariant metric of nonnegative or positive 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 $S^1\times S^3$ that is not a product metric.


Related publications

2005 Repository Open Access
Krishnan Shankar, Kristopher Tapp and Wilderich Tuschmann

Nonnegatively and positively curved invariant metrics on circle bundles

In: Proceedings of the American Mathematical Society, 133 (2005) 8, pp. 2449-2459