A fourth-order dispersive flow into Kähler manifolds

Hiroyuki Chihara; Eiji Onodera

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arXiv · 1308.5542

A fourth-order dispersive flow into Kähler manifolds

Hiroyuki Chihara·Eiji Onodera

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Abstract

We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact Kähler manifold. Our equations geometrically generalize a physical model describing the motion of a vortex filament or the continuum limit of the Heisenberg spin chain system. Our results are proved by using so-called the energy method. We introduce a bounded gauge transform on the pullback bundle, and make use of local smoothing effect of the dispersive flow a little.

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Hiroyuki Chihara, Eiji Onodera. 2013-08-26. A fourth-order dispersive flow into Kähler manifolds. https://arxiv.org/abs/1308.5542

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