Finite-gap solutions of the vortex filament equation: Genus one solutions and symmetric solutions

摘要

For the class of quasiperiodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction, and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. We also prove generalizations of these connections to higher genus.