Fundamental theorems of Lagrangian surfaces in $S^{2}\times S^{2}$

Abstract

Existence and $\mathit{SO}(3) \times \mathit{SO}(3)$-congruence of Lagrangian immersion from oriented 2-dimensional Riemannian manifold to the Riemannian product of 2-spheres are studied. In particular, we will show that two minimal Lagrangian immersions are $\mathit{SO}(3) \times \mathit{SO}(3)$-congruent if and only if the corresponding angle functions are coincide.