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On Helicoidal Surfaces in a Conformally Flat 3-Space

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Abstract

In this paper, we discuss the problem of finding explicit parametrizations for the helicoidal surfaces in a conformally flat 3-space \(\mathbb {E}^3_F\) with prescribed extrinsic curvature or mean curvature given by smooth functions. Also, we give examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in \(\mathbb {E}^3_F\).

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 41566, Republic of Korea

    Chul Woo Lee

  2. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 52828, Republic of Korea

    Jae Won Lee & Dae Won Yoon

Authors
  1. Chul Woo Lee
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  2. Jae Won Lee
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  3. Dae Won Yoon
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Correspondence to Dae Won Yoon.

Additional information

The third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01060046).

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Lee, C.W., Lee, J.W. & Yoon, D.W. On Helicoidal Surfaces in a Conformally Flat 3-Space. Mediterr. J. Math. 14, 164 (2017). https://doi.org/10.1007/s00009-017-0967-x

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  • DOI: https://doi.org/10.1007/s00009-017-0967-x

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