Special Classes of Meridian Surfaces in the Four-dimensional Euclidean   Space
  Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle. 
Georgi Ganchev and Velichka Milousheva
math.DG