Remarks on the Gauss images of complete minimal surfaces in Euclidean   four-space
  We perform a systematic study of the image of the Gauss map for complete minimal surfaces in Euclidean four-space. In particular, we give a geometric interpretation of the maximal number of exceptional values of the Gauss map of a complete orientable minimal surface in Euclidean four-space. We also provide optimal results for the maximal number of exceptional values of the Gauss map of a complete minimal Lagrangian surface in the complex two-space and the generalized Gauss map of a complete nonorientable minimal surface in Euclidean four-space. 
Reiko Aiyama, Kazuo Akutagawa, Satoru Imagawa and Yu Kawakami
math.DG math.CV