Minimal surfaces in S^2xS^2

A general study of minimal surfaces of the Riemannian product of two spheres S^2xS^2 is tackled. We stablish a local correspondence between (non-complex) minimal surfaces of S^2xS^2 and certain pair of minimal surfaces of the sphere S^3. This correspondence also allows us to link minimal surfaces in S^3 and in the Riemannian product S^2xR. Some rigidity results for compact minimal surfaces are also obtained.