Minimal Lagrangian surfaces in $\mathbb{S}^2 \times \mathbb{S}^2$

We deal with the minimal Lagrangian surfaces of the Einstein-Kähler $\mathbb{S}^2 \times \mathbb{S}^2$ surface, studying local geometric properties and showing that they can be locally described as Gauss maps of minimal surfaces in $\mathbb{S}^3 \subset \mathbb{S}^4$ . We also discuss the second variation of the area and characterize the most relevant examples by their stability behaviour.

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Published 1 January 2007