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In the present paper, we study timelike surfaces with parallel normalizedmean curvature vector field in the four-dimensional Minkowski space. Weintroduce special isotropic parameters on each such surface, which we callcanonical parameters, and prove a fundamental existence and uniqueness theoremstating that each timelike surface with parallel normalized mean curvaturevector field is determined up to a rigid motion in the Minkowski space by threegeometric functions satisfying a system of three partial differentialequations. In this way we minimize the number of functions and the number ofpartial differential equations determining the surface, thus solving theLund-Regge problem for this class of surfaces.

Timelike Surfaces with Parallel Normalized Mean Curvature Vector Field in the Minkowski 4-Space