Geodesics of Hofer's metric on the space of Lagrangian submanifolds

• Autores: Hiroshi Iriyeh, Takashi Otofuji
• Localización: Manuscripta mathematica, ISSN 0025-2611, Vol. 122, Nº. 4, 2007, págs. 391-406
• Idioma: inglés
• DOI: 10.1007/s00229-007-0076-4
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• Resumen

  • We study geodesics of Hofer¿s metric on the space of Lagrangian submanifolds in arbitrary symplectic manifolds from the variational point of view. We give a characterization of length¿critical paths with respect to this metric. As a result, we see that if two Lagrangian submanifolds are disjoint then we cannot join them by length-minimizing geodesics.