A third order dispersive flow for closed curves into almost Hermitian manifolds

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Abstract

We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and eliminate the loss of one derivative from the partial differential equation of the dispersive flow.

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Details

  • CRID
    1050861482659369984
  • NII Article ID
    120001224291
  • NII Book ID
    AA00252370
  • HANDLE
    2324/12556
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB
    • CiNii Articles
    • KAKEN

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