Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$,withtheneutralmetricgivenby$(g,-g)$\mathrm{.}Here${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$,and$g$ is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.