Flat surfaces of finite type in the 3-sphere

We introduce the notion of flat surfaces of finite type in the 3- sphere, give the algebro-geometric description in terms of spectral curves and polynomial Killing fields, and show that finite type flat surfaces generated by curves on S2 with periodic curvature functions are dense in the space of all flat surfaces generated by curves on S2 with periodic curvature functions.

Accepted Version

Not peer reviewed