WorkshopsLagrangian surfaces in pseudo-Kähler tangent bundles
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Given an oriented Riemannian surface (Σ,g), its tangent bundle TΣ possesses a pseudo-Kähler structure G that plays most naturally with the canonical symplectic structure Ω. We then focus on surfaces S of TΣ which are both Lagrangian with respect to Ω and minimal or hamiltonian-stationary with respect to G. We first show that if g is nonflat and S is minimal, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R^3 induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS^2. Joint work with Henri Anciaux and Brendan Guilfoyle.
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Pascal Romon
2011-07-05
15:15:00 - 16:15:00
R101 , Astronomy and Mathematics Building
Given an oriented Riemannian surface (Σ,g), its tangent bundle TΣ possesses a pseudo-Kähler structure G that plays most naturally with the canonical symplectic structure Ω. We then focus on surfaces S of TΣ which are both Lagrangian with respect to Ω and minimal or hamiltonian-stationary with respect to G. We first show that if g is nonflat and S is minimal, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R^3 induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS^2. Joint work with Henri Anciaux and Brendan Guilfoyle.
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