2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80882For the class of quasi-periodic 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.36 pages, 8 figures; additional references includedExactly Solvable and Integrable SystemsDifferential Geometrytext