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The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

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Seppi A.

Complex Manifolds

2017

tom 4

nr 1

183-199

Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a symplectomorphism for the area forms of the two hyperbolic metrics h and h' on S induced by the action of p on ℍ2 x ℍ2. Using an algebraic construction related to the flux homomorphism, we give a new proof of the fact that φ∑ is the composition of a Hamiltonian symplectomorphism of (S, h) and the unique minimal Lagrangian diffeomorphism from (S, h) to (S, h’).

Ograniczanie wyników

1 Complex Manifolds

1 Seppi A.

1 2017

Wyniki wyszukiwania

The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry