Abstract
In this paper, we define pedal and contrapedal curves of framed immersions, which can have singularities, in the Euclidean 3-space and investigate the sufficient conditions that they are framed base curves. Moreover, we give the relations among pedal curves, contrapedal curves, evolutes and involutes of framed immersions.
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All data generated or analysed during this study are included in this article.
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Acknowledgements
The authors would like to thank the reviewers for helpful comments to improve the original manuscript. This work was supported by the National Natural Science Foundation of China (Grant no. 11671070).
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This work was supported by the National Natural Science Foundation of China (Grant no. 11671070).
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KY and ML wrote the main manuscript text. EL and DP reviewed and edited. DP fund. All authors have read and agreed to the published version of the manuscript.
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Yao, K., Li, M., Li, E. et al. Pedal and Contrapedal Curves of Framed Immersions in the Euclidean 3-Space. Mediterr. J. Math. 20, 204 (2023). https://doi.org/10.1007/s00009-023-02408-z
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DOI: https://doi.org/10.1007/s00009-023-02408-z