Journal Article Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space

Aiyama, Reiko  ,  Akutagawa, Kazuo  ,  Imagawa, Satoru  ,  Kawakami, Yu

196 ( 5 )  , pp.1863 - 1875 , 2017-10-01 , Springer Verlag
ISSN:0373-3114
NCID:AA11616592
Description
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. © 2017 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg
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