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Almost positive curvature on the Gromoll-Meyer 7-sphere


Author: J.-H. Eschenburg
Journal: Proc. Amer. Math. Soc. 130 (2002), 1165-1167
MSC (2000): Primary 53C20, 53C30; Secondary 57S25, 57R60
Published electronically: September 19, 2001
MathSciNet review: 1873792
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Abstract: D. Gromoll and W. Meyer have represented a certain exotic 7-sphere $M$ as a biquotient of the compact Lie group $Sp(2)$. Thus any invariant normal homogeneous metric on $Sp(2)$ induces a metric of nonnegative sectional curvature on $M$. We show that the simplest such metrics (except the bi-invariant one) induce metrics which have in fact strictly positive curvature outside a subset of $M$ with measure zero.


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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

DOI: https://doi.org/10.1090/S0002-9939-01-06151-2
Keywords: Biquotients, exotic 7-sphere, quaternions, zero curvature set
Received by editor(s): September 28, 2000
Received by editor(s) in revised form: October 23, 2000
Published electronically: September 19, 2001
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society