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Slant helices and isothermic surfaces

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Abstract

In the present paper, we investigate the determinative conditions for the isothermic Hopf cylinders and Hopf tori of spherical helices which are the tangent indicatrices of slant helices. Based on the relationship between geodesic curvature and principal curvatures, the characterizations are obtained by blending the results of inspired references.

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Acknowledgements

The authors are very grateful to the Editor-in-chief and the referee for their constructive, effective, valuable comments which helped us to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Nevşehir HBV University, Nevşehir, Turkey

    Çağla Ramis

  2. Department of Mathematics, Faculty of Science and Arts, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, Turkey

    Beyhan Yilmaz

  3. Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey

    Yusuf Yayli

Authors
  1. Çağla Ramis
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  2. Beyhan Yilmaz
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  3. Yusuf Yayli
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Correspondence to Çağla Ramis.

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Ramis, Ç., Yilmaz, B. & Yayli, Y. Slant helices and isothermic surfaces. Beitr Algebra Geom 59, 145–154 (2018). https://doi.org/10.1007/s13366-017-0352-8

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  • DOI: https://doi.org/10.1007/s13366-017-0352-8

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