Lagrangian Spheres in the Complex Euclidean Space Satisfying a Geometric Equality

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For a Lagrangian submanifold of ℂn with scalar curvature τ and mean curvature vector H, the inequalityholds, and the equality is given only in open sets of the Lagrangian subspaces of ℂn or of the Whitney sphere. In this paper, a one-parameter family of Lagrangian spheres including the Whitney sphere is constructed. They satisfy a geometric equality of type τ = η | H | 2, with η >0, and they are globally characterized inside the family of compact Lagrangian submanifolds with null first Betti number in ℂn

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