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Sequential natural mates of Frenet curves in Euclidean 3-space

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Abstract

Associated with a Frenet curve \(\alpha \) in Euclidean 3-space \(\mathbb {E} ^{3} \), there exists the notion of natural mate \(\beta \) of \(\alpha \). In this article, we extend the natural mate \(\beta \) to sequential natural mates \(\{ \alpha _{1},\alpha _{2},\ldots ,\alpha _{n_{\alpha }}\}\) with \( \alpha _{1}=\beta \). We call each curve \(\alpha _{i},i\in \{1,2,\ldots ,n_{\alpha }\},\) the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve \(\alpha \) with its sequential natural mates \(\{ \alpha _{1},\alpha _{2},\ldots ,\alpha _{n_{\alpha }}\}\).

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Acknowledgements

The authors express thank to the referees for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Arts, Onsekiz Mart University, Çanakkale, Turkey

    Çetin Camci

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48 824-1027, USA

    Bang-Yen Chen

  3. Faculty of Sciences and Arts, Department of Mathematics, Kırıkkale University, Kırıkkale, Turkey

    Kazım İlarslan & Ali Uçum

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  1. Çetin Camci
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  2. Bang-Yen Chen
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  3. Kazım İlarslan
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  4. Ali Uçum
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Correspondence to Ali Uçum.

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Camci, Ç., Chen, BY., İlarslan, K. et al. Sequential natural mates of Frenet curves in Euclidean 3-space. J. Geom. 112, 46 (2021). https://doi.org/10.1007/s00022-021-00610-6

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  • DOI: https://doi.org/10.1007/s00022-021-00610-6

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