Abstract
For a Lagrangian submanifold of Cn with scalar curvature τ and mean curvature vector H, the inequality (τ ≤ n2(n-1)/n+2 |H|2) holds, and the equality is given only in open sets of the Lagrangian subspaces of ηn or of the Whitney sphere (cf. [RU] and also [BCM]). 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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Castro, I. Lagrangian Spheres in the Complex Euclidean Space Satisfying a Geometric Equality. Geometriae Dedicata 70, 197–208 (1998). https://doi.org/10.1023/A:1004959903681
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DOI: https://doi.org/10.1023/A:1004959903681