A metric on S^2 \times S^2 with positive sectional curvature
Simon Brendle, September 15, 2026
We describe a construction of a positively curved metric on S^2 \times S^2. Starting from the standard metric on S^2 \times S^2, we first perform a Cheeger deformation. The resulting metric has nonnegative sectional curvature. We refer to it as a Cheeger-Mueter metric. We then consider a suitable third order perturbation of this Cheeger-Mueter metric and show that the perturbed metrics have positive sectional curvature. This is joint work with Pei-Ken Hung.
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