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Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces whichare one-parameter systems of meridians of a standard rotational hypersurface.On the base of our invariant theory of surfaces we study meridian surfaces withspecial invariants. In the present paper we give the complete classification ofChen meridian surfaces and meridian surfaces with parallel normal bundle.

Special Classes of Meridian Surfaces in the Four-dimensional Euclidean Space