The Tzitzeica surface as solution of PDE systems.
Theory of coverings in the study of Riemann surfaces
For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method...
Tzitzeica theory -- opportunity for reflection in mathematics.