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We construct a special class of Lorentz surfaces in the pseudo-Euclidean4-space with neutral metric which are one-parameter systems of meridians ofrotational hypersurfaces with timelike or spacelike axis and call them meridiansurfaces. We give the complete classification of the meridian surfaces withparallel mean curvature vector field. We also classify the meridian surfaceswith parallel normalized mean curvature vector. We show that in the family ofthe meridian surfaces there exist Lorentz surfaces which have parallelnormalized mean curvature vector field but not parallel mean curvature vector.

Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric