We consider a special class of spacelike surfaces in the Minkowski 4-spacewhich are one-parameter systems of meridians of the rotational hypersurfacewith timelike or spacelike axis. We call these surfaces meridian surfaces ofelliptic or hyperbolic type, respectively. On the base of our invariant theory of surfaces we study meridian surfaceswith special invariants and give the complete classification of the meridiansurfaces with constant Gauss curvature or constant mean curvature. We alsoclassify the Chen meridian surfaces and the meridian surfaces with parallelnormal bundle.
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