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Total Torsion and Spherical Curves Bending

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Abstract

It is well known that the total torsion of a closed spherical curve is zero. Furthermore, if the total torsion of any closed curve on the surface is zero, then it is part of a plane or a sphere. In this paper, we examine the total torsion of a spherical curve during infinitesimal bending. We find the appropriate bending fields and show that the variation of the total torsion of a closed spherical curve is equal to zero. Some examples are considered both analytically and using our own software tool. For figures, we use colors to represent the value of torsion at different points of the curve, together with a colour-value scale.

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Acknowledgements

The authors are supported by the Serbian Ministry of Science, Technological Development and Innovation under the research grants 451-03-65/2024-03/200123 and 451-03-65/2024-03/200124 and by the project IJ-2303 of Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220, Kosovska Mitrovica, Serbia

    Marija S. Najdanović

  2. Faculty of Sciences and Mathematics, University of Niš, 18000, Niš, Serbia

    Svetozar R. Rančić & Ljubica S. Velimirović

Authors
  1. Marija S. Najdanović
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  2. Svetozar R. Rančić
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  3. Ljubica S. Velimirović
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All authors contributed to the manuscript equally.

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Correspondence to Marija S. Najdanović.

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Najdanović, M.S., Rančić, S.R. & Velimirović, L.S. Total Torsion and Spherical Curves Bending. Mediterr. J. Math. 21, 74 (2024). https://doi.org/10.1007/s00009-024-02595-3

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  • DOI: https://doi.org/10.1007/s00009-024-02595-3

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