Almost positive curvature on the Gromoll-Meyer sphere

Jost-Hinrich Eschenburg; Martin Kerin

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arXiv · 0711.2987

Almost positive curvature on the Gromoll-Meyer sphere

Jost-Hinrich Eschenburg·Martin Kerin

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Abstract

Gromoll and Meyer have represented a certain exotic 7-sphere $Σ^7$ 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 $Σ^7$ has strictly positive sectional curvature at all points outside four subvarieties of codimension $\geq 1$ which we describe explicitly.

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Jost-Hinrich Eschenburg, Martin Kerin. 2007-11-19. Almost positive curvature on the Gromoll-Meyer sphere. https://arxiv.org/abs/0711.2987

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