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Almost positive curvature on the Gromoll-Meyer sphere

Eschenburg, J.-H. and Kerin, M. (2008) 'Almost positive curvature on the Gromoll-Meyer sphere.', Proceedings of the American Mathematical Society, 136 (9). pp. 3263-3270.


Gromoll and Meyer have represented a certain exotic 7-sphere Σ7 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 Σ7 has strictly positive sectional curvature at all points outside four subvarieties of codimension ≥ 1 which we describe explicitly.

Item Type:Article
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Date accepted:No date available
Date deposited:15 November 2022
Date of first online publication:23 April 2008
Date first made open access:15 November 2022

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