Good afternoon,


There is an example of a Riemannian metric on $S^2 \times S^2$ of nonnegative sectional curvature that is not a product metric. I know there is one; however, I cannot find a specific reference. Any suggestions?



A Riemannian metric on $S^2 \times S^2$ of nonnegative curvature that is not a product
A discussion of nonnegatively curved metrics on $S^2\times S^2$ can be found in the  [survey](https://aimath.org/WWN/nnsectcurvature/WilkingSurvey.pdf) by B. Wilking, see page 26 and last paragraph on page 25. In particular, there is a one parametric family of metrics of nonnegative curvature on $S^2\times S^2$ which are not moved by any diffeomorphism to a product metric.


