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Cyclic and ruled Lagrangian surfaces in Euclidean four space

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Abstract

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 in the 3-sphere or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the 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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Authors and Affiliations

  1. Department of Mathematics and Computing, Institute of Technology, Tralee, Co. Kerry, Ireland

    Henri Anciaux

  2. Université de Paris-Est Marne-la-Vallée, 5, bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée cedex 2, France

    Pascal Romon

Authors
  1. Henri Anciaux
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  2. Pascal Romon
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Correspondence to Henri Anciaux.

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Anciaux, H., Romon, P. Cyclic and ruled Lagrangian surfaces in Euclidean four space. Bull Braz Math Soc, New Series 40, 341–369 (2009). https://doi.org/10.1007/s00574-009-0015-y

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  • DOI: https://doi.org/10.1007/s00574-009-0015-y

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