Almost positive curvature on the Gromoll-Meyer sphere

Details Almost positive curvature on the Gromoll-Meyer sphere Almost positive curvature on the Gromoll-Meyer sphere

2007-11-19

arxiv.org/abs/0711.2987v1

Mathematics

Differential Geometry

8 pages, 1 figure, to appear in Proc. Amer. Math. Soc

Scientific paper

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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