Pseudospherical surfaces with singularities (Q2362869)

Based on Lorentzian harmonic maps, the author generalizes surfaces of constant Gauss curvature \(-1\) in Euclidean \(3\)-space as pseudospherical frontals, and analyse the singularities of these surfaces by dividing them into those of characteristic and non-characteristic type. He gives methods for constructing all non-degenerate singularities of both types as well as many degenerate singularities, and also gives a method for solving the singular geometric Cauchy problem, which constructs a pseudospherical frontal containing a given regular space curve as a non-degenerate singular curve.