Almost positive curvature on the Gromoll-Meyer sphere

Eschenburg, J.-H.; Kerin, M.

Abstract

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.

Citation

Eschenburg, J.-H., & Kerin, M. (2008). Almost positive curvature on the Gromoll-Meyer sphere. Proceedings of the American Mathematical Society, 136(9), 3263-3270. https://doi.org/10.1090/s0002-9939-08-09429-x

• Journal Article Type: Article
• Online Publication Date: Apr 23, 2008
• Publication Date: 2008
• Deposit Date: Nov 15, 2022
• Publicly Available Date: Nov 15, 2022
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 136
• Issue: 9
• Pages: 3263-3270
• DOI: https://doi.org/10.1090/s0002-9939-08-09429-x
• Public URL: https://durham-repository.worktribe.com/output/1188928