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Article Dans Une Revue Bulletin Brazilian Mathematical Society Année : 2009

Cyclic and ruled Lagrangian surfaces in complex Euclidean space

Résumé

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces.
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Dates et versions

hal-00137761 , version 1 (21-03-2007)
hal-00137761 , version 2 (15-04-2008)

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Citer

Henri Anciaux, Pascal Romon. Cyclic and ruled Lagrangian surfaces in complex Euclidean space. Bulletin Brazilian Mathematical Society, 2009, 40 (3), pp.341-369. ⟨10.1007/s00574-009-0015-y⟩. ⟨hal-00137761v2⟩
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