Pei-Ken Hung

A metric on $S^2 \times S^2$ with positive sectional curvature

We construct a metric on $S^2 \times S^2$ with positive sectional curvature. 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-M\"uter metric. We then consider a suitable third order pertur...