HAMILTONIAN STATIONARY LAGRANGIAN FIBRATIONS

Abstract : Hamiltonian stationary Lagrangian submanifolds (HSLAG) are a natural generalization of special Lagrangian manifolds (SLAG). The latter only make sense on Calabi-Yau manifolds whereas the former are defined for any almost Kähler manifold. Special Lagrangians, and, more specificaly, fibrations by special Lagrangians play an important role in the context of the geometric mirror symmetry conjecture. However, these objects are rather scarce in nature. On the contrary, we show that HSLAG submanifolds, or fibrations, arise quite often. Many examples of HSLAG fibrations are provided by toric Käh-ler geometry. In this paper, we obtain a large class of examples by deforming the toric metrics into non toric almost Kähler metrics, together with HSLAG submanifolds.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01332545
Contributeur : Yann Rollin <>
Soumis le : jeudi 16 juin 2016 - 10:39:23
Dernière modification le : mercredi 11 octobre 2017 - 01:14:15

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  • HAL Id : hal-01332545, version 1
  • ARXIV : 1606.05886

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Eveline Legendre, Yann Rollin. HAMILTONIAN STATIONARY LAGRANGIAN FIBRATIONS. 2016. 〈hal-01332545〉

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