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Ruled surfaces generated by elliptic cylindrical curves in the isotropic space

  • Muhittin Evren Aydin EMAIL logo and Adela Mihai
Published/Copyright: October 27, 2017
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Abstract

In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the isotropic 3-space 𝕀3. We classify such surfaces in 𝕀3 with constant curvature and satisfying an equation in terms of the components of the position vector field and the Laplacian operator. Several examples are given and illustrated by figures.

MSC 2010: 53A35; 53A40; 53B25

Award Identifier / Grant number: A/14/02337

Funding statement: The second author’s research was supported by the DAAD Fellowship for University Professors and Researchers A/14/02337 at Technical University of Berlin, December 2014–January 2015.

Acknowledgements

The second author would like to thank Professor Udo Simon for being her host Professor at Technical University of Berlin and his kind hospitality. Figure 1 in this paper is prepared with Wolfram Mathematica 7.0 and all other drawings with VisuMath (www.visumath.be).

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Received: 2015-01-23
Accepted: 2016-04-27
Published Online: 2017-10-27
Published in Print: 2019-09-01

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