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Proceedings of the American Mathematical Society

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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

M. Kerin
Affiliation: Department of Mathematics, University of Pennsylvania, 209 S 33rd St., Philadelphia, Pennsylvania 19104

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