Minimal surfaces in S^2xS^2

TL;DR

This paper explores minimal surfaces in the product space S^2xS^2, establishing a correspondence with minimal surfaces in S^3 and S^2xR, and presents rigidity results for compact minimal surfaces.

Contribution

It introduces a local correspondence between minimal surfaces in S^2xS^2 and pairs of minimal surfaces in S^3, linking different geometric contexts.

Findings

Established a correspondence between minimal surfaces in S^2xS^2 and S^3.

Linked minimal surfaces in S^3 and S^2xR.

Derived rigidity results for compact minimal surfaces.

Abstract

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.