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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost positive curvature on the Gromoll-Meyer sphere


Authors: J.-H. Eschenburg and M. Kerin
Journal: Proc. Amer. Math. Soc. 136 (2008), 3263-3270
MSC (2000): Primary 53C20, 53C30
Published electronically: April 23, 2008
MathSciNet review: 2407092
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09429-X
PII: S 0002-9939(08)09429-X
Keywords: Biquotients, Lie groups, left invariant metrics, quaternions
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
Article copyright: © Copyright 2008 American Mathematical Society