Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space
Annali di Matematica Pura ed Applicata(2017)
摘要
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.
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关键词
Gauss map, Exceptional value, Minimal surface, Minimal Lagrangian surface, Primary 53A10, Secondary 30D35, 53C42
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