Isometric Immersions of L2 into L4
2006 - J. A. Aledo, J. A. Gálvez, P. Mira
Differential Geometry and its Applications 24, 613-627 (2006).
We give a global Weierstrass representation for isometric immersions with flat normal bundle from domains of the Lorentz plane into . This representation relies on the choice of two holomorphic data on a Riemann surface, and the integration of a hyperbolic linear differential system. As applications, we give classification results and construct complete examples in explicit coordinates by exact integration of the differential system for some particular choices of the holomorphic data.