Nonnegatively and positively curved invariant metrics on circle bundles
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- by Krishnan Shankar, Kristopher Tapp and Wilderich Tuschmann PDF
- Proc. Amer. Math. Soc. 133 (2005), 2449-2459 Request permission
Abstract:
We derive and study necessary and sufficient conditions for an $S^1$-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 $S^1\times S^3$ that is not a product metric.References
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Additional Information
- Krishnan Shankar
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
- Email: shankar@math.ou.edu
- Kristopher Tapp
- Affiliation: Department of Mathematics, Bryn Mawr College, Philadelphia, Pennsylvania 19010
- MR Author ID: 630309
- Email: ktapp@brynmawr.edu
- Wilderich Tuschmann
- Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einstein- strasse 62, D-48149 Münster, Germany
- MR Author ID: 350718
- Email: wtusch@math.uni-muenster.de
- Received by editor(s): October 15, 2002
- Received by editor(s) in revised form: April 14, 2003
- Published electronically: March 21, 2005
- Additional Notes: The first author was supported in part by NSF grant DMS–0103993.
The third author’s research was supported by a DFG Heisenberg Fellowship. - Communicated by: Wolfgang Ziller
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2449-2459
- MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-05-08135-9
- MathSciNet review: 2138888