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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

Equivariant maps into Anti-de Sitter space and the symplectic geometry of H^2xH^2

Résumé

Given two Fuchsian representations ρ l and ρr of the fundamental group of a closed oriented surface S of genus ≥ 2, we study the relation between Lagrangian submanifolds of Mρ = (H^2/ρ_l(π_1(S))) × (H^2/ρ_r(π_1(S))) and ρ-equivariant embeddings σ of S into Anti-de Sitter space, where ρ = (ρ_l ,ρ_r) is the corresponding representation into PSL(2,R) × PSL(2,R). It is known that, if σ is a maximal embedding, then its Gauss map takes values in the unique minimal Lagrangian submanifold Λ ML of Mρ. We show that, given any ρ-equivariant embedding σ, its Gauss map gives a Lagrangian submanifold Hamiltonian isotopic to Λ_ML. Conversely, any Lagrangian submanifold Hamiltonian isotopic to Λ_ML is associated to some equivariant embedding into the future unit tangent bundle of the universal cover of Anti-de Sitter space.
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Dates et versions

hal-01675383 , version 1 (04-01-2018)

Identifiants

Citer

Francesco Bonsante, Andrea Seppi. Equivariant maps into Anti-de Sitter space and the symplectic geometry of H^2xH^2. Transactions of the American Mathematical Society, 2019, 371 (8), pp.5433-5459. ⟨10.1090/tran/7417⟩. ⟨hal-01675383⟩

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