It was shown by J. C. Langer and D. A. Singer in their influential 2007 paper  that real algebraic curves can be interpreted as trajectories of meromorphic quadratic differentials defined on appropriate Riemann surfaces. The goal of this note is to suggest a more elementary approach to this problem that is based on the classical complex analysis. To demonstrate how our approach works, we apply it to the simplest non-trivial case of real algebraic curves; i.e. to conics.
- Quadratic differential
- Real algebraic curve