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Weingarten Affine Translation Surfaces in Euclidean 3-Space

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Abstract

By solving certain (partial) differential equations we give the total classification of Weingarten affine translation surfaces in three dimensional Euclidean space \(\mathbb {E}^3\). Explicitly, a Weingarten affine translation surface in Euclidean 3-space is the minimal affine Scherk surface or the surface with flat metric.

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Authors and Affiliations

  1. Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Jeju, 690-756, Korea

    Seoung Dal Jung

  2. Department of Mathematics, Northeastern University, Shenyang, 110004, People’s Republic of China

    Huili Liu

  3. College of Life Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Yixuan Liu

Authors
  1. Seoung Dal Jung
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  2. Huili Liu
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  3. Yixuan Liu
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Corresponding author

Correspondence to Huili Liu.

Additional information

H. Liu was supported by NSFC (No. 11371080); Joint Research of NSFC and NRF; partially supported by the Chern Institute of Mathematics and Northeastern University. S. D. Jung was supported by NRF-2015R1A2A2A01003491.

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Jung, S.D., Liu, H. & Liu, Y. Weingarten Affine Translation Surfaces in Euclidean 3-Space. Results Math 72, 1839–1848 (2017). https://doi.org/10.1007/s00025-017-0737-x

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  • DOI: https://doi.org/10.1007/s00025-017-0737-x

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