Flat surfaces of finite type in the 3-sphere
University College Cork
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.
Differential geometry , Finite gap , Flat tori
McCarthy, A. 2014. Flat surfaces of finite type in the 3-sphere. PhD Thesis, University College Cork.