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arXiv · 1606.02376

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

Reiko Aiyama·Kazuo Akutagawa·Satoru Imagawa·Yu Kawakami
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Abstract

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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Reiko Aiyama, Kazuo Akutagawa, Satoru Imagawa, Yu Kawakami. 2016-06-08. Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space. https://doi.org/10.1007/s10231-017-0643-6

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