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

Abstract

We investigate minimal surfaces in products of two-spheres S_p²×S_p², with the neutral metric given by (g,-g). Here S_p² ⊂ 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.