Timelike Surfaces in the Lorentz-Minkowski Space with Prescribed Gaussian Curvature and Gauss Map
2006 - J. A. Aledo, J. A. Gálvez, J. M. Espinar.
Journal of Geometry and Physics 56, 1357-1369 (2006).
In this paper we obtain a Kenmotsu-type representation for timelike surfaces with prescribed Gauss map in the three-dimensional Lorentz–Minkowski space . We use such representation in order to classify the complete timelike surfaces with positive constant Gaussian curvature in in terms of harmonic diffeomorphisms between simply connected Lorentz surfaces and the universal covering of the de Sitter Space.