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Abstract: Consider the complex linear space C^n endowed with the canonicalpseudo-Hermitian form of signature 2p,2n-p. This yields both apseudo-Riemannian and a symplectic structure on C^n. We prove that thosesubmanifolds which are both Lagrangian and minimal with respect to thesestructures minimize the volume in their Lagrangian homology class. We alsodescribe several families of minimal Lagrangian submanifolds. In particular, wecharacterize the minimal Lagrangian surfaces in C^2 endowed with its naturalneutral metric and the equivariant minimal Lagrangian submanifolds of C^n witharbitrary signature.



Author: Henri Anciaux

Source: https://arxiv.org/







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