Almost positive curvature on the Gromoll-Meyer sphere
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- by J.-H. Eschenburg and M. Kerin PDF
- Proc. Amer. Math. Soc. 136 (2008), 3263-3270 Request permission
Abstract:
Gromoll and Meyer have represented a certain exotic 7-sphere $\Sigma ^7$ as a biquotient of the Lie group $G = Sp(2)$. We show for a 2-parameter family of left invariant metrics on $G$ that the induced metric on $\Sigma ^7$ has strictly positive sectional curvature at all points outside four subvarieties of codimension $\geq 1$ which we describe explicitly.References
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Additional Information
- J.-H. Eschenburg
- Affiliation: Institut für Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
- Email: eschenburg@math.uni-augsburg.de
- M. Kerin
- Affiliation: Department of Mathematics, University of Pennsylvania, 209 S 33rd St., Philadelphia, Pennsylvania 19104
- Email: mkerin@math.upenn.edu
- Received by editor(s): April 30, 2007
- Published electronically: April 23, 2008
- Additional Notes: The second author would like to thank the University of Pennsylvania for financial support.
- Communicated by: Jon G. Wolfson
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3263-3270
- MSC (2000): Primary 53C20, 53C30
- DOI: https://doi.org/10.1090/S0002-9939-08-09429-X
- MathSciNet review: 2407092