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Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface
| Content Provider | Semantic Scholar |
|---|---|
| Author | Anciaux, Henri Guilfoyle, Brendan Romon, Pascal |
| Copyright Year | 2008 |
| Abstract | Given an oriented Riemannian surface (Σ, g), its tangent bundle TΣ enjoys a natural pseudo-Kähler structure, that is the combination of a complex structure J, a pseudo-metric G with neutral signature and a symplectic structure Ω. We give a local classification of those surfaces of TΣ which are both Lagrangian with respect to Ω and minimal with respect to G. We first show that if g is non-flat, 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 or R1 induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS or TH respectively. We relate the area of the congruence to a second-order functional F = ∫ √ H2 − K dA on the original surface. 2000 MSC: 53A10 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0807.1387v2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Congruence of squares Hamiltonian (quantum mechanics) Motion Pseudo brand of pseudoephedrine Symplectic integrator |
| Content Type | Text |
| Resource Type | Article |
