TITLE: A Riemannian metric on $S^2 \times S^2$ of nonnegative curvature that is not a product
QUESTION [11 upvotes]: 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?

REPLY [11 votes]: A discussion of nonnegatively curved metrics on $S^2\times S^2$ can be found in the  survey 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.