A metric on $S^2 \times S^2$ with positive sectional curvature
- Published
- Source
- arXiv
- Paper number
- 956
- Field
- Research
- arXiv ID
- 2608.19068
Key points
- It proved by construction that the product of two spheres, S²×S², admits a metric with positive sectional curvature everywhere.
- Starting from the standard metric, it applied a Cheeger deformation to obtain a nonnegatively curved Cheeger-Müter metric, then added a third-order perturbation.
- Using the structure of the zero-curvature planes remaining at each generic point and the vanishing first variation of the perturbation, it made even the last flat directions positive.
- It resolved a longstanding existence problem in differential geometry, expanding the concrete examples of positively curved 4-dimensional spaces.
- Several calculations in the proof rely on MATHEMATICA, and accompanying code is provided, making independent verification of the symbolic calculations and execution of the code important for confirming the result.
Paper links
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