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Enveloids of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane

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Abstract

We define \(\theta \)-isogonal curves for one-parameter families of Legendre curves. The \(\theta \)-enveloid for a given one-parameter family of Legendre curves is a plane curve that cuts each member of the family in the same constant angle \(\theta \). As an application, we consider the definition of involutoids of frontals from the view point of \(\theta \)-enveloids. Moreover, we consider the properties of normal envelopes.

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Acknowledgements

The authors would like to thank the reviewers for helpful comments to improve the original manuscript. The first two authors are partially supported by National Natural Science Foundation of China (Grant No. 11671070) and the last author is partially supported by JSPS KAKENHI (Grant No. JP 20K03573).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Enze Li & Donghe Pei

  2. Muroran Institute of Technology, Muroran, 050-8585, Japan

    Masatomo Takahashi

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  1. Enze Li
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  2. Donghe Pei
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  3. Masatomo Takahashi
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Contributions

Conceptualization, EL, DP and MT; Writing-Original Preparation, EL; Writing-Review and Editing, DP and MT; Funding Acquisition, DP and MT. All authors red and approved the final manuscript.

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Correspondence to Donghe Pei.

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Communicated by Pablo Mira.

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Li, E., Pei, D. & Takahashi, M. Enveloids of Legendre Curves in the Unit Tangent Bundle over the Euclidean Plane. Bull. Malays. Math. Sci. Soc. 45, 3011–3041 (2022). https://doi.org/10.1007/s40840-022-01320-1

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  • DOI: https://doi.org/10.1007/s40840-022-01320-1

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