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arXiv · 2609.12882

A Two-Stage Construction of Positive Curvature on the Gromoll-Meyer Sphere

Shengtao Guo·Ethan X. Fang·Junwei Lu
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Abstract

We construct an explicit one-parameter family of smooth metrics on the Gromoll-Meyer exotic seven-sphere, converging in $C^\infty$ to a fixed further Cheeger deformation of the Eschenburg-Kerin metric and having strictly positive sectional curvature for all sufficiently small positive parameter values. The first perturbation preserves the totally geodesic flats of one zero-plane family while making curvature positive near the other; the second removes the remaining zero curvature. The metric and the proof were discovered by the Odin Automatic AI Research Agent.

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Shengtao Guo, Ethan X. Fang, Junwei Lu. 2026-09-11. A Two-Stage Construction of Positive Curvature on the Gromoll-Meyer Sphere. https://arxiv.org/abs/2609.12882

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