Riemann surfaces with symmetries arise in many studies of integrable systems. We illustrate new techniques in investigating such surfaces by means of an example. By giving a homology basis well adapted to the symmetries of Klein's curve, presented as a plane curve, we derive a new expression for its period matrix. This is explicitly related to the hyperbolic model and results of Rauch and Lewittes.
Journal of Physics A Mathematical General
- Pub Date:
- October 2010
- Mathematics - Algebraic Geometry;
- Mathematical Physics;
- Mathematics - Representation Theory
- 16 pages 5 figures. Final version makes connection with other known period matrices